Buying a badge gets you into the convention hall and, when it's open, into the exhibit hall (which is inside the convention hall). There are many things that require you to not only have a badge, but to also have an event ticket (which usually, but not always costs money – GTG's state of the company event, for instance, is a $0 ticket).
Things that require tickets: A vast array of organized games – board games, RPGs, CCGs, tabletop minis, LARPs, etc, plus a few scattered other things like panels, and various music/theater performances.
Things that don't require tickets: Costume contest, paint and take, demoing games at booths in the exhibit hall, doing the quizzes set up around the convention, finding people to play an informal game on the floor or in a hotel lobby, etc, a room showing movies, and a variety of other small activities.
Getting some generic tickets is a good way to prepare yourself for wandering around looking for something interesting and then being able to sit down and join if the game isn't full.
Researching what's available and getting specific tickets is a good way to make sure you get to do specific things you want to do.
Wandering around with a game you like and inviting strangers to play with you is a good way to make new friends.