A Minecraft server is a host computer that provides a Minecraft world to which other players can connect. It isn't necessary to access a server to play, as Minecraft also operates as a single player game.
Although it's possible for any player to set up a Minecraft server, it can be a complex task. There are already thousands of servers available around the world that cater to different styles of play. For example, a player who prefers to use the creative aspects of the game can choose a server geared toward that style of play, while a player who wants to use Player Versus Player combat can use a server dedicated to that playing style.