A Lacrima typically appears as a pale blue crystal rock when found in situ. Normally, Lacrimae are found to be refined for purpose, being reshaped into spherical ball shapes typically.
Lacrima can be used for various purposes; it can serve as a power source for vehicles, a tool for long-range communications (i.e. Communications Lacrima), to the point where it can be used as a weapon of sheer combat (e.g. Explosive Lacrima).
The peak of its usage, however, lies in Dragon Slayers themselves, who implant Lacrimae in themselves in order to utilise Dragon Slayer Magic; the Dragon Lacrima. Mages that achieve this are often referred to as the Second Generation of Dragon Slayers. There is also the Third Generation, who on top of having been taught the magic by the dragons themselves, use Lacrimae of the same element in order to strengthen their magic's power even further.
In general, though, Edolas is more reliant on Lacrimae as to compensate for their lack of mana mages need to actually perform magic. As such, their usage of these substances acts as the testament of their technological advancement, and is much more advanced than Earthland with regards to the development of Lacrima's usage for many different means.