A character is the person that a player controls in their adventures throughout the World of Warcraft. There are multiple choice to make in create one's character, including choice of class, race, gender/appearance, and playstyle. Once created, your character is your avatar for your adventures in the world.
As you continue to play, your character will gain experience that in turn makes them more powerful. They will acquire reputation with various groups in the world, and they will acquire new magical equipment to survival the more dangerous places.
The game focuses entirely on your adventures with your character, however what you do with it is your own business. You will encounter other players doing their own things. PCs, or player characters, are the other people you meet that are controlled by a human being. By default, their name will appear over their head in one of several colors.