I have filed as independent for the past two years. And now my parents want to claim me on thier taxes again. What is that going to do to me?

If you don’t provide more than half of your support they can claim you so you have to check the box on your return saying that someone else can claim you. As a dependent you will not get a stimulus payment and can’t claim education credit. 

Sounds like you qualified as their dependent the last 2 years.  Even if they didn't claim you, you were supposed to check the box that's says you can be claimed.