Obsidian is volcanic glass, formed when a silica-rich lava cools too fast for crystals to grow, and its two great uses both follow directly from the fact that it is glass rather than rock.
The first is the edge. Glass fractures conchoidally, and a fresh obsidian edge can be a few molecules thick, far finer than any metal blade. Mesoamerican workers developed a prismatic blade technology of great sophistication, pressing long parallel-sided blades from a prepared core, and obsidian tools and weapons were the basis of the region's cutting technology in the absence of iron. Sources were controlled and traded over long distances; the distinctive green obsidian of the Pachuca source in central Mexico is recognisable on sight and is found across Mesoamerica, which makes it an unusually good tracer of exchange networks.
The second is the surface. Polished obsidian gives a dark reflective mirror, and mirrors were made from it in Anatolia by the seventh millennium BCE and in Mesoamerica throughout its history. The Aztec deity Tezcatlipoca, whose name means smoking mirror, is depicted with one. The obsidian mirror in the British Museum associated with John Dee is Mexican in origin and reached England after the conquest, which places a Mesoamerican ritual object at the centre of an Elizabethan scrying practice.
Obsidian absorbs water very slowly through its surface over time, and measuring the depth of the hydrated rind gives an approximate date for when a flake was struck. That technique is a genuine archaeological method with real limitations.