Nothing on the Internet delivers news faster than Twitter. Every other platform is either too slow (websites with CMS's and editors), or too filtered (Facebook or chat apps, on which posts are private by default).
If you want to know what's happening right now, Twitter will give you better results than anything else, including a Google search. Tweets famously beat an earthquake from Virginia to New York, fulfilling an XKCD joke. And it's almost all searchable by the public in real time.
So that's one thing: it's a close as you're going to get to a real-time tap in the zeitgeist.
Another use is comedy; you get everything from corny puns and "dad jokes," to multi-year character humor arcs, to biting political humor, all in one place, as fast as you want it.
Another is the ability to drill down into a wide variety of subcultures. Various niches within politics, programming, sports, finance, etc. all have robust conversations going on constantly, and many of them internationally.
Candidly, it took a long time for me to get Twitter. Ultimately for me the secret was to follow a bunch of folks I might like, see what they said, unfollow the ones I didn't like, and then follow the folks who the others (the ones I kept) retweeted.
I spend more time on Twitter now than any other social network or app. And I only really started "gettting it" a year or two ago.