For the most part? They’re just a bit of fun to encourage contributions and bit of friendly rivalry. They also help you identify users who are active and may be able to help.
It’s not just best answers that earn them however, other actions do as well. Completing any such action automatically awards a specified number of points - such as posting your question. Tim is the ultimate decision maker when it comes to what thing earns how many points. The Forum Moderators are the primary decision makers when assigning Best Answers, however Forum Volunteers such as myself also hold that power - we can assign answers instantly at our discretion.
As for what you get? Well, if you reach certain thresholds… Something good may happen…
Or in my case, roughly every six months, something good does happen. :D