New board games are often on display in the vendor hall. You can wander up, learn to play, and buy it there. But for a popular game that takes a while to play, someone else will probably already be using it. You might have a long wait for a turn.
An event ticket guarantees you a spot to play the game at a specific time.
Events for older board games are often hosted by some random person not associated with the company that sold the game. You are welcome to bring your copy of Settlers of Catan and run it as an event.
Likewise, most RPG events are campaigns written by the GM.
Ticketed events also include crafts, seminars, and experiences like True Dungeon.
There are a limited number of tickets to each event, so if there's a game you definitely want to play, you should buy a ticket.
You don't necessarily have to decide right now, but the longer you wait, the more likely the event is to be sold out.
You can also buy "generic" tickets and use them to jump in on a game that isn't sold out, or had a no-show, or can accommodate an extra player.