It was apparently a tiebreaker to me getting my first job. They liked how I documented technical stuff on my blog.
And the process of writing something up is always great for making sure I know what I'm talking about. I want to write a paragraph about a certain aspect, but it's only then that I realize that I'm not actually sure about it. So I investigate more until I'm sure.
And don't underestimate the value of a library of blob posts. When someone asks you to explain something you can reply that while you're perfectly happy to have a chat about it, you actually have a blog post about it that should give them a good understanding.
I've found that people really appreciate getting such a complete answer, and (since your question seems to focus on value you get) helps you become known as "the expert". Like "hey, do you know if it's possible to do X?" -- "Oh yeah, here's a step by step guide".
And a blog is a better memory than your brain. You'll find yourself remembering knowing something, but no longer knowing it. With a blog you can just go back to the past you that was an expert in this, and refresh your memory.
You won't get the value from the first post alone. But after a while the value adds up. It's like how you don't get stronger from one day at the gym, but from putting in the time.
People reading my blog have also commented or emailed me with more info, or questions, and I've later met them at conferences and even jobs, and we'd have further chats on the topic.
Writing a blog post can mark the end of a small project, so is a motivator, too.
Led to jobs: check.
Increased learning: absolutely check.
Brought new connections: check.
Vanity: No more than a job well done, and feeling useful to others, or at least future me.