I dunno how long you've been on HN, but around 2007-2008 there were a bunch of HighScalability articles about Twitter's architecture. Back then it was a pretty standard Rails app where when a Tweet came in, it would do an insert into a (replicated) MySQL database, then at read time it would look up your followers (which I think was cached in memcached) and issue a SELECT for each of their recent tweets (possibly also with some caching). Twitter was down about half the time with the Fail Whale, and there was continuous armchair architects about "Why can't they just do this simple solution and fix it?" The simple solution most often proposed was write-time fanout, basically what this article describes.
Do the math on what a single-server Twitter would require. 150M active users * 800 tweets saved/user * 300 bytes for a tweet = 36T of tweet data. Then you have 300K QPS for timelines, and let's estimate the average user follows 100 people. Say that you represent a user as a pointer to their tweet queue. So when a pageview comes in, you do 100 random-access reads. It's 100 ns per read, you're doing 300K * 100 = 30M reads, and so already you're falling behind by a factor of 3:1. And that's without any computation spent on business logic, generating HTML, sending SMSes, pushing to the firehose, archiving tweets, preventing DOSses, logging, mixing in sponsored tweets, or any of the other activities that Twitter does.
(BTW, estimation interview questions like "How many gas stations are in the U.S?" are routinely mocked on HN, but this comment is a great example why they're important. I just spent 15 minutes taking some numbers from an article and then making reasonable-but-generous estimates of numbers I don't know, to show that a proposed architectural solution won't work. That's opposed to maybe 15 man-months building it. That sort of problem shows up all the time in actual software engineering.)