When you "Follow" a person (or company/entity) on Twitter their posts get added to your main page so it curates your personal interests (you don't have to be following someone to join their discussions, it just keeps you up with them). They get a notice of a new follower and if they choose to follow you in return it's called a "Follow Back". So, say I get notification that someone has followed me, generally it is someone who has liked my comments through common interests so I will look at their page and make sure they aren't a spammer/scammer/prat and follow back. Celebrities and companies generally don't follow back though some will follow back a lot or everyone (often done by assistants), some do choose their own follow backs and a few are actually very interactive with their followers.
When an individual account like me posts (tweets) a comment any interaction is much like a topic in this forum. When an account like CNN tweets the interaction is more like a comment section under an article on their site.