One method to play against another human involves playing on different machines, connected throgh a network link. This can be local, but usually this refers to an online capability, connecting players through the Internet.
In the late 1990’s, some emulators had this functionality, but back then, it took a powerful machine (by the standards of the day) to even play most fighting games on an emulator, and most computer users weren’t on anything better than a dial-up modem (if that), limiting the potential use of networking to play fighting games.
With the release of Capcom vs. SNK 2 on both Dreamcast and PS2 in 2001, networked play began to be an official feature of many official fighting game releases intended for home-use systems.