You don't need to know all the airport codes or abbreviations, I don't think there's anyone that would know them all!
There's a few simple abbreviations you'll need to learn but you'll pick them up very quickly in the work environment when everyone around you is using them.
Just try to enjoy the training (not easy, I know) and you'll pick up everything once you get out there doing the job. When I first started at dispatch I had all my initial training then had to wait 2-3 weeks for my references etc to get my pass before I started shadowing etc, in which time I'd forgotten virtually everything I'd been taught. As others have said, you start learning once you get out there
