What does it mean when you have a dream within a dream?

I dreamt that me and my favourite teacher were hiding in the basement from a hurricane. And at the last moment I decided to move to a different area in that basement, which lead to her being killed because of me. I felt like it was my fault and I screamed very loud. I ended up waking up but I was still in a dream. So then I dreamt again that I woke up screaming. And finally I actually woke up in real life. What do you think this means? I have been under quite a lot of stress lately as well.