A time crystal is a kind of quantum system. It changes in a repeating way over time, even when it is in its lowest-energy state (the ground state). It does this without taking in energy from outside.
An ordinary crystal has atoms in a pattern that repeats in space. A time crystal has a pattern that repeats in time.
Time crystals may one day be used as quantum memory.
Writers of science fiction sometimes use the name "time crystal" for imaginary objects. These are not the same as real time crystals.