A quick, semi-personal connection between two people across a distance. This can further be boiled down as humans interest in connection and conversation.
It turns out that Twitter, due to the social network (both existing and being one sided) solves this problem better then text messaging. So really it evolved text messaging.
This is much like the quote by Henry Ford "If I had asked people what they wanted, they would have said faster horses." Ford was not "solving a real problem" -- the problem of transportation had already been solved since the dawn of time. He was evolving the solution to a faster, more convenient method.