Well, in the loosest definition of the word, everything we experience is real. We are really experiencing it.

But there is an easy way to test whether a dream is real in the strictest sense of the word. Do the things that happen in the dream have consequences in our waking life? If you run into a wall in a dream, do you wake up with bruises?

What's likely to happen is you will probably go through the wall unharmed. In fact, these types of reality checks are useful for anyone wishing to become lucid in a dream. Try to do something in the dream that you can't normally do in waking life, and then you'll know whether it's a dream.

Another way to tell whether dreams are real is to ask people you spoke to in the dream whether they remember the dream too.