What happens next?

Probably another stupid question from me but as a FTB I'm trying to learn as much about the process as possible. We applied for our mortgage last week and I've now been told our application has went to "full offer" and that the paperwork has been sent to both our solicitor and us. After reading lots of horror stories on here I don't think I'll believe the property is actually ours until we get the keys.

So what can I expect to happen now? We had already agreed a move in date as a condition of our offer so is it now just the legal work involved to insure that happens?

By the way, we're in Scotland.