In the TV series The Mandalorian beskar is a metal for forging different things. Why is this metal important for the Mandalorians?
Is it because of the origin of the metal or its properties? Or is it something more spiritual, like a ritual with their armor, for example?
The answer depends, as many Star Wars questions do, on whether you're looking at Canon or Legends, but both have some of the same points. Since you're asking in regards to The Mandalorian, I'll give the Canon one first.
Beskar in Canon is a particularly strong type of steel used, or at least produced, almost exclusively by Mandalorian smiths. It's a traditional material used most commonly in the production of a Mando'ad's armor but weapons and other items may be made from it as well. Its extreme durability (being all but invulnerable to blasters and lightsabers, for example), makes it highly prized by Mando'ade, though not all armor is made from it. The Tribe in The Mandalorian seem to be considerably more spiritual or even religious than other depictions, to the point that they outright declare weapons to be "part of their religion", so they have a considerable respect and deference to the use of Beskar. It should also be noted that by the time of the TV show, the Empire has taken over Mandalore and routed production of Beskar into its own stores, as well as stolen quantities of it as seen in the show, in effect stealing Mandalorian cultural heritage (the forging of Beskar was considered an art and secret among the Mandalorians). There may be an analogue there to the Third Reich stealing all manner of items of cultural and religious (and personal) significance from Jewish families et al prior to and during the Second World War.
In Legends, Beskar is slightly different. Most notably, it's not an alloy or steel as it's depicted in the show, but a unique form of "iron" that was only found on the planet Mandalore. (While it could be alloyed with other materials to enhance its properties; it didn't have to be.) As such, only Mandalorian smiths had the knowledge and resources to forge it and it was consequently very rare throughout the Galaxy and indeed on Mandalore itself. As with Canon, the Empire had a vested interest in acquiring quantities of the material and initially entered into a treaty with Mandalore for exclusive mining rights and information on how to forge it in exchange for considerable contracts with the MandalMotors shipbuilding firm. However, the Empire's rule over Mandalore became increasingly tyrannical and ultimately resulted in the enslavement of the Mandalorians and the strip-mining of the majority of the world's Beskar veins. It was not until after the Empire fell that Mandalorians were able to discover new deposits of Beskar and resume their cultural traditions regarding the metal; presumably, Beskar throughout the Galaxy was returned in one degree or another to Mandalore for use by its people.
Both depictions of the metal were highly valued by the Mandalorian culture, primarily because as warrior races, it was a traditional material that was one of the key reasons for their strength in handling enemies up to and including the Jedi Knights. Likewise with both depictions, the Empire's theft of the material from Mandalore and its eventual subjugation of the Mandalorian people made recovering Beskar a matter of regaining cultural heritage that was nearly destroyed. However, Mandalorian culture in Canon is still somewhat sketchy; for example, whether or not The Tribe represents a more widespread system of belief or ideology among the Mandalorians at large or is just relegated to that particular group (evidence from other Canon sources would indicate the latter, such as the rule regarding removing one's helmet) is somewhat unclear.
Beskar is important for multiple reasons, two of which can be seen in The Mandalorian.
Although in canon, Beskar was not so rare and was used by various tribes/groups, it became very rare, following the events of Empire's downfall. The Empire massacred the Mandalorians and took almost all of the Beskar.
UNKNOWN MANDALORIAN: These are the spoils of the Great Purge. The reason that we live hidden like sand rats. Our secrecy is our survival. Our survival is our strength. Our strength was once in our numbers. Now we live in the shadows and only come above ground one at a time. Our world was shattered by the Empire, with whom this coward shares tables.
Chapter 3: The Sin
After the Empire's downfall, the Beskar was most likely lost as seen throughout the season; even the Armorer sounds surprised when she sees Mando's bounty for the child's delivery.
Further in Chapter 3: The Sin, when Mando's armor is damaged after the events with the Mudhorn, Mando delivers the child to the Empire to collect his bounty.
THE CLIENT: Is it not the Code of the Guild that these events are now forgotten? That Beskar is enough to make a handsome replacement for your armor. Unfortunately, finding a Mandalorian in these trying times is more difficult than finding the steel.
Chapter 3: The Sin
In Chapter 5: The Gunslinger, when Mando and Toro Calican are on their way to capture Fennec Shand, an Assassin, she attacks them with an MK rifle.
THE MANDALORIAN: Get down! - (grunts) -
TORO CALICAN: Mando! (grunts) What happened?
THE MANDALORIAN: Sniper bolt. Only an MK-modified rifle could make that shot.
TORO CALICAN: Are you all right?
THE MANDALORIAN: Yeah. Hit me in the beskar, and at that range beskar held up.
Chapter 5: The Gunslinger
It's a little bit of both.
On a practical level it's an extremely durable metal, producing some of the best weapons and armor. You see on multiple occasions that "The Mandalorian's" armor easily deflects blaster bolts. 
But it does clearly have a spiritual side also. The Mando shows solemn reverence while the smith forges his new gear. And in Star Wars: Rebels Sabine Wren has this to says about her armor.
"The armor I wear is 500 years old. I reforged it to my liking, but the battles, the history, the blood, all lives within it, and the same goes for every Mandalorian."
