Not to be confused for the creator or the video game, obsidian is in its most common form a black, volcanic rock primarily formed of silicon dioxide, formed when lithic flows cool in a rapid fashion. Its usage is extremely common in fiction, particularly of the speculative or historical sort, in part due to its comparatively common nature in general: anywhere you find a volcano, you're likely to find some, and silicon is one of the most common elements on Earth. So why is it so popular?
For a start, obsidian has a tendency to fracture in a fashion quite similar to glass. Any media which depict obsidian as being in any way a 'strong' material are engaging in a research failure, although it is modestly resilient to damage when properly handled: it's extremely brittle when thin, particularly compared to metallic alloys. Where this becomes useful, however, is that when you carve or chip obsidian down, you can make blades and arrowheads out of it, along with other tools, something which was commonplace in the Stone Age. This led to its use as a very common and valuable trade good, a practice which can be deduced based on the composition of the material itself: since each source has a slightly different mineral composition, one can track down precisely where it came from.
Obsidian is the primary source of the Absurdly Sharp Blade: when it's fractured, the resultant edges can be as little as 3 nanometers thick, capable of microthin slicing. Even today, obsidian knives are used for certain surgical procedures in animal research, and work has been done to determine if it's a viable mechanism for performing eye surgeries; glass and diamond, two of the other cases of Absurdly Sharp Blade, are oftentimes used as well. Beware this fact, though: just like the proverbial 'glass knife', an obsidian blade doesn't last long: its edges become dulled almost instantly in use, albeit not to the point of uselessness.
Another reason for obsidian's ubiquity in media is its trademark color. Black knives, swords or arrowheads are by their nature implicitly cooler than some 'simple' steel, at least by today's standards. Because of this, obsidian has been led to associations with demons (either in their destruction, or as their tools), though often obsidian has also been shown to be the weapon of choice for, say, a fire god. Historically, obsidian has also been used in the creation of all manner of other tools: bowls, plates, and even some early proto-mirrors. If you see an obsidian mirror in a work, you can probably guess that the creators have done their research.
Oh, and don't forget, it came out of a volcano. How cool is that?