job offers... or not?

I just got done with my second interview and at the end of the interview, the hiring manager said "I'm offering you the job" and I said I wanted it and signed some paperwork. She said hr will contact me in a week for another interview, which would be like a background check and such... my question is, do I have this job? can I turn down another offer I have for a different job now? sorry just confused and I don't want to lose that other offer until I know I have this one.
It is likely you have the job. However, you can always rescind your acceptance if you get another offer. Be prompt in telling the first manager that you have found a position more suitable to your needs at this time and be effusive in your thanks for the opportunity.
thank you, i guess what im worried about is that HR will decide not to hire me. Im not even sure if they do that lol. I dont want to turn down the other offer until I hear from HR at the other hospital, but I don't want to lead the first hospital on too long