A server is a computer on the internet used in playing the game. A server determines the actions of each NPC; it keeps track of where each character is, what they look like and what they are doing; and it remembers your character's name, level, costumes and everything else while you are logged off.
The more players using a server, the more work it has to do. If too many people use the same server at the same time it has a hard time keeping up with all their actions and things might slow down or get jerky on the screen. You select which server you want to use when you log on.