I understand that it is short for retroactive continuity, but could someone explain the concept and provide some examples to illustrate?
Any sufficiently complex setting introduces the opportunity for plot holes: this is compounded when there are multiple writers (in the case of TV shows and movies) and when there are multiple works set within the same world (in the case of franchises and series).
Many times, because of the level of detail, writers and authors are unaware of how their stories interact with the rest of the setting's canon, and in other cases, they choose to ignore it for the sake of telling a good story.
In these cases, the maintainers of the setting have two choices: they can choose to ignore the problem or they can choose to introduce retroactive continuity (a retcon) to correct the problem: both have their benefits and drawbacks, but a retcon is generally introduced to placate fans who would otherwise be alienated by the lack of attention to detail.
A good example of retconning exists in Star Trek to explain the difference between the old-style Klingons, who look and act like humans, and modern-style Klingons, who look and act markedly differently. The real reason for this was because the older series lacked the makeup budget to make them look truly different, but the later series did not have such a restriction.
For over a decade, they ignored the problem, but retconned a reason for it in the prequel series Star Trek: Enterprise: the Klingons suffered a debilitating malady that caused them to look and act like humans. In this case, the retcon is used to explain a plot hole introduced to fix problems with the setting.
Another example would be the Star Wars franchise: in A New Hope, we learn that the Force is some all-encompassing thing that binds everyone in the Universe and Jedis are almost magical in their ability to attune themselves to it. But in The Phantom Menace, also a prequel, we learn that Jedis are able to tap into the force because of high concentrations of microscopic parasitic organisms called midichlorians.
However, in this case the retcon was introduced because it appears Lucas wasn't aware of or forgot about the original basis for the Force.
Another example from Star Wars - the infamous usage of 'parsec' by Han Solo when boasting about the speed of the Millenium Falcon.
She made the Kessel Run in twelve parsecs
It was eventually retconned in one of the expanded universe books (about 10 or so years later) by explaining that spice smugglers had to skim past a black hole cluster - the faster the ship, the closer they could drop into the clusters gravity field, and the shorter the distance they have to travel to get around it.
Another example can be found in comic books. Marvel Comics created a character called "The Beyonder" in their comic limited series 'Secret Wars'. The character was originally the single most powerful being in the Marvel Universe. The Beyonder was shown to be more powerful than all the other 'Cosmic Beings' in the Marvel Universe; The Living Tribunal, Eternity, Death, Celestials, Galactus, Chaos and Order etc. The character however was later "retconned" and down-powered to be an immature 'Cosmic Cube' and not the omnipotent being he thought he was. All this was later revealed in a comic of the Fantastic Four. The Beyonder later merged with The Molecule Man to become a sentient cosmic cube. The character had undergone further changes after that.