I applied for a job at the hospital, had the interview, The HR called told me all the benefits, the pay, and the hours I would be working. She said she only needs to the the background check and she will call me back, does this mean I have the job?

If you pass the background check without any criminal record or anything like that, then yes. However if you have some sort of criminal record, that would jeopardize your chances greatly.

How do you think you did in the interview? They'll base their decision on that, too.