A kief box (or kif box) is a box that is used to collect kief from buds. It's basically a box with a mesh screen over it; the buds or leaves are carefully broken up on the screen, and the finer kief goes through the screen into the box. It's important not to crush the buds too much, and especially to not rub the buds on the screen like it's a cheese grater. Doing this contaminates the kief with bits of leaf, so it defeats the purpose.

I'm on the lookout for more details, descriptions, pictures, etc. Watch this space.