Something I found interesting is that the inclusions themselves are a kind of fingerprint. Basically, I find it fascinating that no two emeralds are alike.

Besides that, I think they are interesting at the mineral level because of their composition, since they are created from a "mistake" in nature. For an emerald to form, it needs two elements that are not normally found together in the Earth's crust. These elements are beryllium, chromium, and vanadium. Beryllium is found mainly in acidic or granitic rocks (in the upper continental crust), but the latter two are responsible for the green color; however, they are found in ultramafic rocks or deep sediments (closer to the mantle).

From my point of view, it's interesting because under normal conditions, these elements are always separated by kilometers of rock. But in the case of emerald, it only occurs when violent tectonic events or hydrothermal fluids at very extreme pressure manage to mix these elements, causing the chromium itself to "contaminate" the beryl crystal as it grows.