Have you experienced waking up only to realize that you are still trapped within another dream? It seems like a trap because it gives you the feeling of not being able to get out of the dream world.
On a more specific and practical note, you may also think that you have already waken up that you are in no hurry to wake up for real. This may make you miss your intended waking time.
What dreaming within a dream means
When you have a dream within another dream, it means that your subconscious is dealing with something hidden and serious. This may be something that is not easily revealed in dreams that are nearer the surface.
Waking up into another dream may be thought of as a false awakening. It may seem more like a vague memory rather than a false awakening. It will make you wonder if you have actually waken up earlier. One example of such an awakening is going for a pee and not being able to do so.
There are too many obstacles like not being able to find a toilet or not being able to pee when you try. When you wake up for real, you find yourself still wanting to go for a pee. False awakenings involve real morning rituals.
This makes this part of your dream very believable, making you confused as to whether it happened or not.
Knowing when you are dreaming within a dream
You can use the lucid dreaming technique for any dream you want to control. This is when you try to make things happen in your dream instead of being a helpless bystander. This may help you know better when you are dreaming or not.
You should try to remember both the dream within a dream and the dream you wake to during a false awakening. See for yourself if the false awakening is trying to make you forget the main dream. If so, maybe you are meant to forget that main dream.
Dreams help you remember and forget. Those that help you forget are protecting you from potentially damaging information or memory.