Solved a real problem: sending text messages to a group.
Later, it allowed people to get semi-personal access to people they admire.
Later, it allowed people to get semi-personal access to people they admire.
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.
Responding to a phone call on a train during rush hour. Saying "I'm almost there", or "Ill be 5 minutes late" without getting dragged into a conversation in a crowded public space.
There's an infinite variety of cool stuff we can build, but what will have the biggest payoff for my time now, what can I and my team members execute best on right this moment.