When a player has been playing tabletop wargames or building model kits for a while, he (or she) will eventually accumulate a collections of unused model parts, old toys, parts of display models, pieces of junk, and other things that remain from previous modeling projects.
Few gamers will actually throw all this stuff away, and will instead put it all in a box or drawer for future use. Y'know, just in case. This is known as a Bitz Box. Even when it's a collection of boxes, bags, piles, filing cabinets, cupboards and so forth.
The phrase comes from Warhammer 40,000 and, like a surprising amount of player jargon, is derived from the Orkz, in this case the parts and junk a Big Mek uses in his work. (Ork armies are a great way to clear out the techy-looking stuff from one's Bitz Box, as they love welding "gubbinz" onto their machines more or less at random). Some players believe that you have achieved true "orkiness" when pouring glue into the bitz box and shaking it out creates a functional model (Games Workshop GT player Jason Enos first suggested this to supreme studio Ork Adrian Wood and from there it passed into legend). Chaos can help with spare anatomy.
It also sounds better for gamers to talk about their bitz than for them to stand around discussing their junk.
Sometimes when gamers meet, they'll swap bitz to get whatever they're after. Some places like The War Store will sell gamers the bitz they want. And quite often, an email request to a manufacturer such as Airfix or Revell can get you additional or replacement parts, sometimes for free if the company is at fault and the box has been packed incorrectly with parts omitted. Revell and Airfix sometimes charge a small fee for extra parts, but this is usually a modest sum to cover postage and packing.
Model makers outside the tabletop gaming world, such as Airfix kits or model railway layouts, generally use a more pedestrian term like 'spares bin' or 'scraps box'. The principle remains generally similar, however.