1. Literally, to wave to someone when parting. Wave goodbye to your friends, sweetie. They're at the window.

2. To lose or end something, especially suddenly; to be forced to accept such a loss or end. You were caught drinking on school property? Well, you can wave goodbye to your brand new car, mister! After the final horse lost its race, I waved goodbye to all the money I'd won that day at the track. You do realize that you'll be waving goodbye to all the health insurance benefits the company has to offer if you decide to work as a freelancer?