A laptop battle is an electronic music competition. Just a laptop - no external MIDI controllers, no synths, no nothing (well, except an external sound card). Which means you mostly have keys as triggers and possibly your trackpad as an XY controller.
Contestants face each other head-to-head, each playing a 3-minute track, then the audience decides which track is better. It's single-elimination style. Culminating in a final battle between the two "best" contestants.