You can find the BMX bottom bracket at the junction of your frame's seat- and down-tubes.
It consists of two BMX bottom bracket bearings, one on each side. Your pedals are fitted trough it, allowing allows your pedals and chain to spin.
There are two kinds of BMX bottom bracket bearings. The first one is called sealed bearings in short SB. You will find this kind of bearings on quality bikes.
The other one is called ball bearings, in short BB, and is unsealed. This version is often found on the complete BMX bikes for beginner riders.
There're 4 kinds of bottom bracket: American, Mid, Spanish, and Euro. Each one of them indicates different sizes of the BMX bottom bracket bearing.
The specific size of the bottom bracket will only fit in frames with the same BMX bottom bracket shell.