The brain is more active at night because when you're sleeping your brain is in the process of repairing itself and still processing memories and processing other thoughts as well.
Your brain at night being more active is the result of the brains trillions of nerve cells literally rewiring themselves.
During the night when you're asleep there are pronounced changes in the electrical activity of the brain which is evidence that your brain is rewiring itself.
If you're worried about things your mind may not shut off at night and keep you awake.
In that case you may need to take sleeping medicine to help you fall asleep and stay asleep or try avoiding thinking about things that worry you.
Also try thinking of nice things that could happen or think of happy memories that happened to you years ago.