> I still have no idea what the value propostion of Twitter is
I despise twitter, but let me take a shot at this.
Twitter offers users an audience. The short messages and the hashtags means that in the ocean of input, there is a relatively high chance your message will be seen. The retweeting and the framework for an actual fanbase means that, with the right procedures, becoming "twitter-famous" is not horrendeously hard (compare to "realworld-famous" which is often a whole career investment).
The existing userbase and popularity of twitter guarantees that it isn't awkward or obscure to say "Follow me on twitter here", which strengthens what the platform offers.
How it became popular in the first place is a bit more obscure. Obviously it has a lot to do with how it limits the user's input and forces everyone to adopt a casual tone; this fits well with people who don't want to put a lot of thought or effort into a single message, and likewise when reading a user's message (Which is understandable. In a time where there are massive, endless amounts of information at your fingertips, you instinctively tend to wander closer to clickbait headlines than to 3 page articles. Most of us here have seen this a lot on Reddit and even HN).
My guess is that twitter will eventually die out when something more concrete will come along; these days all it takes is the right recipe and the right marketing so it's a decent bet that it could come out of Facebook or a similarly popular platform. Hell, it could come out of Twitter itself. In the mean time, what it offers is somewhere for people to rant and shout without feeling like they are not being heard.