Multiplayer is one of the two gamemodes in Terraria, with the first being singleplayer wherein one plays alone and has the ability to pause the game at command, and the second; Multiplayer, which has the ability play with multiple players at once, but not the ability to pause (In order to not disrupt the gameplay of others). In order to play multiplayer in Terraria, two things are required, the first being a host and the second being the players themselves. The host provides the players with a server which again, has a world in it wherein the players play. The host has the ability to communicate to the players, save the map, close the server, set the time of day and the ability to kick or ban players. If the host attempt to run server in PC with the console or iOS device, the console or iOS device will not connect to PC servers.
There is also an item which is only accesible in multiplayer, namely the Team Dye
Players can find servers to play on in this Terraria server list: Terraria-Servers.com. Servers are also presented on the official server forums, usually with more information.