When you follow someone it just makes it easier to stay in contact with them. You can get to their recently asked questions or recently answered questions and see what they are up to. If you didn't follow them, it would take forever finding them again.
It keeps you "Connected". If you find someone who ask's good questions, or someone who gives good answers, you can follow them. You can then go on the "Connections" tab, and see activity from the person who you are following.
When you follow someone, it means you either like their answer, find their answer funny, respect them, like their personality, or anything else. You can have "friends" on ask.com, which is fun! You can also chat with them and answer their questions. :)