I assume that you are travelling on a single ticket (sold to you in one transaction). The fact that the airline has sold you the ticket means that they think that the connection time is enough to make your next flight. They will transfer your checked luggage from one plane to the next. (Of course, keeping your carry-on luggage with you is your responsibility.)
However, 37 minutes is a very short connection, especially for a large airport like Atlanta. You will need to move quickly through the terminal. If your first flight is delayed at all, you probably not be able to make it. However, if this happens, the airline will rebook you onto a later flight. A quick search indicates that Delta flies from Atlanta to Miami a dozen times each day, so this may not be that bad - if you miss your connection, it is likely that Delta will put you on a later flight not too much later.