Dreams are defined as series of thoughts, images, and sensations occurring in a person's mind during sleep.

Real is defined as actually existing as a thing or occurring in fact; not imagined or supposed.

These series of thoughts, images, and sensations occurring in a person's mind during sleep are actually existing as a thing or occurring in fact; not imagined or supposed. So dreams are real.

Note that all of this occurs in the mind, though. If the act of you dying comes across your mind while sleeping, it doesn't mean you actually die.