Mega Man was a physical robot in the original games. In Battle Network, he was now an AI in a computer and you sent him to do battle with enemy AI and viruses on networks in the game.
It was branded Rockman EXE in Japan, and NT Warrior (i.e. Net Warrior) in the US anime, only. The "network" refers to the internet and the internet of things heavily featured in the games, in which you battle viruses; hence "Battle Network."
They had a PVP mode you could do by linking with other players called Net battling. Despite it being a GBA series, (with some DS releases) it still has a strong online PVP community to this day, as well as a fan game that has been in strong development for a few years now.