A Utopia is the "perfect" society, which does not exist and is in fact impossible. Think John Lennon's "Imagine." The reason a utopica is not possible is because there always has to be some kind of governing body ruling the society, and this would lead to oppression in some way and, thus, would not be perfect.
Dystopian societies are those that have tried to become utopias. They are often depicted in novels and movies. Anthem by Ayn Rand is the perfect example of a dystopian society. In trying to treat everyone as equal, the people lost their individuality and face severe consequences if they try to be different in any way or think for themselves. This book, and others like it, are written specifically to show what would happen if we tried to create a utopian society.