Made infamous by Sigmund Freud, the idea is that we spend one third of our lives dreaming about what we would like to do. Our rational brain suppresses these feelings.
On the other extreme, our brain is just as active in certain sleep stages. These neural firings express themselves in dreams. There are no deep hidden emotions behind them.
Somewhere in between lie recent studies that show that dreams are important in memory, learning and emotions. If you sleep without dreaming these qualities will suffer. For example, rat studies in 2001 showed how while dreaming they replayed solutions to mazes to commit them to their long-term memory.