It's multi-machine scheduling, basically. Given N resources and M consumers, how can I fit all M consumers most efficiently, while using the minimum N?

The bin metaphor is that you imagine one or several bins on the floor, and a bunch of things to place in bins. Binpacking is just playing tetris to make sure all your things are packed into as few bins as possible, because bins cost money.

https://en.wikipedia.org/wiki/Bin_packing_problem