A Mirai (Future) Crystal is an item created by a being's strong desires of the future. Once crystallized it can grant the user (the being that it originated from) additional powers when used. The extent of these powers is unknown as (currently) the factors of Mirai Crystal creation are very much unknown and their numbers are few.
Few of these crystals have been "created", and all of those that have been "created" have been found at Aether Farms. The common theme of their "creation" is people that are very sure of their future. It seems this strong sentiment, combined with the high concentration of Aether, causes the Aether to crystallize and form these stones.
It is possible that other energies could create these stones if the right conditions are present, such as having a high concentration of the energy.
What a Mirai Crystal can do is greatly varied, and mostly unknown at this point, but it is tied to the character's desires for the future. The crystal focuses on what "can be" instead of "what is". It is possible that it could give the user temporary access to powers they do not currently have, but could have in the future if that is their strong desire.
Regardless of its effects the crystals can only be used once per thread, and have a cooldown period of 1 to 3 threads.