One reason why we are likely to wake up during a dream is due to the nature of REM sleep, the sleep phase in which most dreams occur. In REM sleep, our brain activity is near the waking level, but our body remains "asleep" or paralyzed so that we cannot realize our dreams in bed. Because our brain is so active at this stage, it can sometimes essentially wake us up.
As Girardin Jean-Louis, Ph.D., Professor of Population Health and Psychiatry at NYU, explains: "Some dreams with vivid content can temporarily wake you up. This can be the case when someone is being followed or the feeling of flying or of falling onto a platform. "
This does not mean that external influences like bedroom noises cannot wake you up while you are dreaming, but it seems that some dreams also have a way of raising our awareness.