Twitter's core is the home timeline: the reverse-chronological (or ranked) feed of tweets from everyone you follow. Posting a tweet is a tiny write; reading timelines is a firehose — reads outnumber writes by more than an order of magnitude, so the whole design is about precomputing each user's feed instead of recomputing it on every open.
The defining crux is fan-out: when you tweet, how does that tweet reach the home timelines of all your followers? Push it eagerly at write time, pull it lazily at read time, or both? And what happens when the author is a celebrity with ~100M followers — one tweet becoming a hundred million timeline writes? That hot-user problem is what separates a toy answer from a real one, and it forces a hybrid fan-out strategy.