Follower appears to be the new Diablo III name for the Diablo II mercenaries.
Little is yet known about how mercs will be handled in Diablo III. The D3 team has said there will likely be hireable mercs, but they've given no information about how powerful these mercs will be, how they will be obtained, if they'll get an AI upgrade, or if they'll be able to wear equipment as the D2 mercs were.
Besides the hireable mercs, there are various NPCs to be found in the dungeons who will team up with your character for short durations. Players will find or rescue NPC warriors of various types, and some of these will tag along to help out, or give your character an errand-style quest, asking you to help them find the rest of their patrol. These sort of NPCs can not be controlled; they fight with their own AI and you are unable to heal them or give them equipment to wear.