Vibranium is nowhere near the hardest or strongest metal in the Marvel Universe. Its inherent strength has little to do with why it is highly prized as part of an armor package. Instead, it is the underlying properties of the meta-material which creates its fantastic value and makes it one of the most sought-after materials on Marvel's Earth.
Found only in the African nation of Wakanda, the technologies pioneered through the study of Vibranium give Wakandan science an extraordinary advantage making it one of the most technologically-advanced nations on Earth.
Defenses made with Vibranium are extremely tough, durable, and extremely stress-tolerant. In the Marvel Cinematic Universe, Vibranium alloys might be some of the strongest metals on Earth (so the claim does have a degree of merit in the MCU, if no place else).
The secluded nation of Wakanda, the only reputable source of Vibranium A on Marvel Earth.
NOTE: There is very little real science involved in the meta-material known as Vibranium in the Marvel comics and Marvel Cinematic Universe. If such a material existed with these properties, its value would be without measure. With that said, we will discuss the capacities of the material in conjunction with its depictions in Marvel franchise materials.
Don't get me wrong, Vibranium IS an impressive metal but not because of its inherent strength. To have an understanding of why it makes a great armor you need to have a little background on this alien meta-material. I use the word meta-material because it exhibits abilities far outside the norm of normal elements found in nature such as iron, gold, osmium or other natural metals found on the periodic table.
What is Vibranium A?
Vibranium is an extraterrestrial material, (element, compound, alloy, meta-material - its actual nature is, like many super-materials in comics, not clearly defined) found in its greatest concentration in the African nation of Wakanda.
While Marvel will give a variety of answers, the extraterrestrial material called Vibranium (also known as Vibranium A) acts mostly like a metal; it is hard, durable and can be bonded with other metals in metallic alloys. These alloys allow the metal to be even more durable and suitable for use in armors.
In the Marvel Cinematic Universe, Vibranium alloys are used in the development of Captain America's shield created by Howard Stark. Stark claimed to have used all of the freely available Vibranium ever collected in the world (known to him, outside of the African nation of Wakanda.) It is suspected that Wakandan Vibranium was stolen and sold to Howard Stark.
The unpainted, Vibranium alloy shield of Captain America presented to Steve Rogers during World War II.
Why Vibranium matters
Where most metals have only their durability to offer as a defensive measure, Vibranium and alloys of the metal have an extra meta-material property not found in any metals on Earth: The harder you hit Vibranium, the stronger it gets (until it breaks)...
Vibranium absorbs vibration or the transfer of kinetic energy used by weapons and bullets, i.e. when striking an armor or shield made of Vibranium, that kinetic energy is absorbed and stored within the molecular bonds of the material, temporarily.
Any energy absorbed does not pass through to the object beneath it. In the Marvel Universe, this means if you strike an object made of Vibranium, nothing happens because the metal absorbs the kinetic potential and disperses it among the metallic bonds of the material, holding the energy and releasing it slowly (and quietly).
Sonic weapons or any attack which uses vibration are completely harmless to Vibranium Alloys. This means bullets and other weapons which deliver kinetic energy will also fail to harm materials made of, or with, sufficiently applied Vibranium.
Not only does Vibranium absorb the mechanical energy, it increases the strength of the material making it stronger and more damage-resistant. However, there is a threshold and once the material has absorbed its threshold of energy, if it cannot release this stored energy in a timely fashion, it will be destroyed (though the energy will not be released violently unless redesigned and altered to do so by scientific processes.)
Technically, this would be applicable to anything which increases molecular movement in a material as well. This means Vibranium should offer some degree of protection against any attack which causes metals to heat up, since heat is the increasing of energy between molecules. There is likely to be a required amount of Vibranium present to gain these benefits, but that is a closely guarded secret of Wakandan science.
The Black Panther's armored clothing protects him using a Vibranium mesh weave, which reduces damage from physical attacks or attacks which rely on the delivery of kinetic energy. This does not mean he can't be harmed, it simply means the attack is blunted reducing its damage. In Civil War, we watch the Black Panther get struck by multiple medium-caliber machine-gun rounds to no effect.
Where does Vibranium originate?
While it has not been confirmed, Vibranium is believed to be an extraterrestrial material found in the greatest concentration in the Marvel Earth nation of Wakanda. Since the material has rarely left the continent, most scientists of the Marvel Universe have no familiarity with the material or its extensive physical properties.
The scientists of Wakanda have the most experience with their version of the material and have managed to create many applications which have been used in military applications within the country and is used primarily in a defensive role by the royal family of Wakanda.
Vibranium comes in two known varieties, Vibranium A and Vibranium B. Each has differing properties. Until now, we have only discussed Vibranium A. There has been no confirmation of the existence of Vibranium B in the Marvel Cinematic Universe (except for the scratching of Captain America's shield by the Black Panther's claws...see below).
Vibranium B (Anti-Metal Vibranium)
There is a second, little known version of Vibranium, an isotope perhaps, dubbed Anti-metal Vibranium (also called Vibranium B). This anti-metal version of Vibranium can, with just a touch, disrupt the metallic bonds of any common metals not protected by force fields.
One touch of Anti-metal Vibranium and normal metals unzip, losing both cohesion and strength. This substance is also believed to be alien in origin and found only in a exotic location known as the Savage Land found on the Antarctic continent.
The Savage Land: The Official Handbook of the Marvel Universe #9 (1983)
Whether normal Vibranium can be converted into Anti-metal is unknown, but the Wakandans do have small supplies of this Savage Land Vibranium on hand and have equipped the Black Panther with it.
The material coats his claws and often other weapons he uses, allowing him to tear through metallic substances with little effort. Materials made with Vibranium or Adamantium may have some degree of resistance to Anti-metal due to their advanced and unusual meta-material properties (such as Captain America's shield).
Vibranium: Wonder Material
In the MCU we have seen Vibranium do or be a part of some amazing feats:
Captain America deflects a strike from Thor's hammer and creates a shockwave which flattens a forest for a few hundred feet in every direction.
Captain America uses the shield which should stop bullets from moving to instead bounce off the shield to strike a shooter.
Captain America bounces an energy blast shot from Iron Man off of his shield.
Captain America can throw his shield, bounce it off a number of surfaces or targets and have it return to him, despite, or perhaps because of, the vibranium in his shield.
Ultron makes a body of Vibranium and becomes incredibly tough; he's able to fight the entirety of the Avengers to an effective standstill.
Black Panther makes an armor mesh suit which renders him effectively bulletproof, and perhaps allows him to destroy metallic defenses with his clawed hands.
It is even suggested that the Vision's body may be composed of some hereforeto unknown synthetic variation of Vibranium in his cellular structure, adding to his durability and possibly responsible for him being alive.
- Vision is a powerful, synthetic being born from a Vibranium-laced body created by Ultron and Helen Cho, programmed by Tony Stark and Bruce Banner using J.A.R.V.I.S.-based codes, and activated by the Mind Stone that was hidden inside the Scepter. (As depicted in Avengers: Age of Ultron)
Vibranium appears to have a wide array of capabilities which defy easy explanation; in some cases, its abilities may even appear contradictory (See: Captain America's MCU shield).
The best thing to be said about it scientifically is this: It's only a movie. Don't take it too seriously. You will drive yourself crazy trying to find a Unified Vibranium Theory which will make it all reasonable.
Within the Television-related MCU: (shared by @CalebHines)
Agents of SHIELD has also utilized vibranium on several occasions.
The hexagonal panels lining the walls of the Bus' Interrogation chamber are said to be "made of a silicon carbide-coated Vibranium alloy" which allows them to contain gifted.
The identical-looking walls of safe house cabin where Daisy stayed after terrigenesis, are undoubtedly the same material. Banner designed it to withstand the Hulk, and a Hulk-print is seen in one of the panels. This must have occurred before the Avengers, since Captain Rogers also spent time there after being defrosted.
The small, cubical "Toolbox" database that Fury gave Coulson after SHIELD's demise was also protected by a Vibranium alloy shell.
It's a safe assumption (though not certain) that Vibranium is used to some extent in the construction of the white hexagonal panels of season 3's Containment Modules. These were designed by Fitz in response to the Inhuman outbreak, and are described as being "made out of adaptive material, so it can contain all sorts of powers."
Apocrypha on the strongest materials in the Marvel Universe:
In the canon comic Marvel Universe, the most durable materials in the Universe are extraterrestrial meta-materials made by advanced societies, with the top of the food chain likely belonging to beings such as Galactus, the Watchers or the Celestials. These cosmic beings have the most advanced sciences in the known universe, so their material science should eclipse just about anyone else's anywhere.
Beings such as Thanos (who have lots of time on their hands, are super-geniuses and don't mind reverse engineering other people's more advanced sciences). Advanced races such as the Kree, Skrulls, Shiar and many other spacefaring species may have ships made of super-dense or super-strong alien alloys. This includes the Asgardians. They also have the benefits of utilizing energy fields to augment their material science.
On Earth, the Adamantium-Vibranium alloy shield of Captain America is considered nigh-indestructible, only beings capable of manipulating cosmic forces can damage it and then the super-hard, molecularly rigid, virtually indestructible metal known as Adamantium shows up on the list. Analogs of Adamantium include the wickedly radioactive Carbonadium, which makes it less desirable as an armor.
Vibranium alloys, depending on what materials it's mixed with would probably fall somewhere around this point: As hard and strong as any known Earth materials can get (tungsten, carbon fibers, titanium alloys) with the added benefit of increased vibration resistance and integrity.
