(I'm bringing this up because I want to write about "time crystals", and to do that....)
The key physics points: When placed together under the right conditions, the building blocks of a crystal spontaneously join together and assemble into the crystal structure. While space has the same properties in every location ("invariance under continuous translation") and in every orientation ("invariance under continuous orientation"), the crystal environment doesn't. Instead, the crystal has discrete translational symmetry (each lattice site is equivalent), and other discrete symmetries (e.g., mirror symmetry about some planes, or discrete rotational symmetries around some axes). This kind of spontaneous symmetry breaking is so general that it happens in all kinds of systems, like plastic balls floating on reservoirs. The spatial periodicity has all kinds of consequences, like band structure and phonon dispersion relations (how lattice vibration frequencies depend on vibration wavelengths and directions).