Crystal has repeatable structure over space. Its lattice is the same shape over and over again.

Time crystal is a kind of crystal that has repeatable structure over time. It just means it changes its "shape" in a repeated fashion over time. Usually an external force is required to force a crystal to change its shape over time such as with the piezoelectric effect. Time crystal is supposed to just keep changing its "shape" over time by itself. In the Yale case, the changing of "shape" is the flipping of the nuclear-spin magnetization periodically.