A crystal is normally thought of as a solid piece of material with a regularly repeating geometric atomic structure. When I think of solid crystals, I usually think of silicon dioxide, quartz. The study of crystal structure, crystallography, has relatively quietly given us huge scientific breakthroughs. Rosalind Franklin created the first image of DNA using crystallographic techniques. It is worth mentioning that Rosalind Franklin has not received due recognition for her work - more here.
So, I've said a little about solid object crystals in space. What then might a real-world "time crystal" be?
Objects, often particles and their constituents, can be represented as having a "world line" which is the path an object traces through x/y axes of space and time. A common example given to illustrate the concept shows the difference between the orbit of the Earth around the sun (which is elliptical) and the world line, which is an open helix, because the Earth does not ever return to the same point in time, although it may occupy the same position in space relative to the sun.
The hypothetical structure - time crystal - assumes that human minds possess properties that most other objects do not. Those of you familiar with Vonnegut have encountered the idea that human minds can travel through time in more than one "direction". Billy Pilgrim of Slaughterhouse 5 becomes dislocated in time as a metaphor for the effects of PTSD.
A time crystal is formed when a mind returns to a point in space and experiences the present and one or more other point of time simultaneously. When this happens, one might imagine that the world line of the mind in question branches off from the main line and loops backward. The loop is a metaphor, but the mind and the point in space, form a structure that we might struggle to directly perceive with the naked eye, but which exists nonetheless.