Oh good lord...
Think of Twitter like ICQ/IM... If you found or had a funny video, pic, topic, news article, ect shared with you or you would share it with someone in the office, then share it with Twitter.
Then if you use a chat/im client to help you, other than twitter directly, you can have conversions with people, like here on gfy... but in a 140 chars or less, which often ends up going to email if it's anything good.
Someone posts a topic/article, you rt or reply to them, they reply to you, others reply, you can add a #hastag so everyone talking can join in, if they want.
I've gotten some pretty crazy convo's going on Twitter before, about all types of topics. I never see my main chat, spammers, ect.. but I've talked with PGA pros, celebs, ceo's of big corps, down to just normal people like us trying to make a dime.
It's a different kind of social, more disconnected and responding back a day or two later about a topic you were talking on, isn't uncommon, so topics can fire back up in an instant.