Boxing is phreaking. Which is pretty much hacking the phone system.
The best box was probably a blue box, though these were obsolete in the early 90's. They exploited the 2600Hz frequency (where the mag 2600 got it's name). It was the frequency used to control CCITT trunks (for international calls) so you get free calls.
Steve Wozniak mass produced them and sold them at uni, then made a nice computer
Red box produces the same tones as dropping money into a payphone, giving you free calls. Also obsolete (there are ways around it).
Black box stopped people being charged for calling you.
Many other boxes existed, but nearly all are obsolete, the main aim was to get free calls!