Why do we dream?

It may help to explain what a dream is.

A dream is believed to be just a bunch or random signals combined in a mosh posh of brain activity. Basically random parts of your brain activate in a random fashion and the signals from these parts, memory, imagination, taste, touch, so forth all combine into your dreams.

As Kreeos said no one knows why we dream, though its known that the majority (not all) dreams occur during REM sleep and that we do need REM sleep, it is very vital to our normal conscious processing.

The major theory as to why we dream is that we dream in order to sort through and store information that we obtained during the day. So to decide what we need to keep and through away.

Another theory is that dreams allow us to heal somehow, its known that most of your healing both physical and mental occurs during REM sleep.

It's also believed that dreams may be a side effect of your brain periodically preforming "tests" to increase performance and find "bad spots" that it needs to repair.

There are several hypotheses but there's insufficient evidence to claim that we know why we dream. Short answer, as of right now nobody knows for sure.