I am having trouble getting my head around this. I usually flame people who do this, but could someone explain in small non-solid-state-physics words as to what it is. The usual sources are no help and most articles define it in terms of equations which I don't know and do not need to know (being a chemist).

Have you done much inorganic chemistry?
The theory behind X-ray crystallography covers some of this (reciprocal space, primitive cells, Bravais lattice, etc)...
If you want I can try to find my old notes, but I only just passed the subject so it may not be the best.