A server allows other players to connect over the internet either directly or through a private network.
Terraria allows you to host a server by selecting Multiplayer, then 'Host & Play'. Though, you may also host using the 'TerrariaServer.exe' included in the game's folder.
When joining a game you may either join via Steam by right-clicking someone on your friends list and selecting 'Join Game', or join via IP by typing the external IP and port of the server you're trying to connect to.
- Pay attention to the server rules to avoid any problems. Respect the admins and other players.