Usually, matter is motionless at its resting state and only has potential energy until kinetic energy is introduced to it.
For example, a ball at rest is chock-full of 'potential energy', and when it's kicked, that energy is converted to 'kinetic energy', the energy of motion.
But time crystals actually move at their 'resting state' or their 'ground state' - that's when atoms have the lowest amount of energy. They're like a ball that is forever in motion.
In other words, they are always unstable, down to the atomic level. They are the first non-equilibrium matter ever created!
MIT Technology Review: Physicists Create World's First Time Crystal
APS Physics: Viewpoint: How to Create a Time Crystal