I still don't know what a Hashtag is or does.

Think of the hashtags as a forum. Normal forums, i.e. flood, community etc no longer exist; you click on the hashtag & view the threads tagged with it as if it were a forum. The format is a hybrid of Twitter, Tumblr & Reddit in many ways. I'd love it if it wasn't Bungie. Bungie's forums served a very different purpose to what this new system will lead to.

What about this reminds you of Reddit?

You can subscribe to different subreddits and they all appear on your front page at the same time.

I wouldn't call tags subreddits.

What's the difference? The only one I can think of is you can add multiple hashtags to a single thread.