Mastodon isn't a startup - it's not even a company. It's a framework, like phpBB forums were (are, I guess). Basically, it's a way that anyone with a web server can set up a Twitter-clone site, but - thanks to the ActivityPub protocol - all those twitter-clones can talk to each other, making the whole universe of Mastodon instances functionally one giant social network.

Mastodon:Twitter::IRC:Facebook Messenger

Practical answer:

Mastodon is a Twitter clone that's currently pretty nice and enjoyable by virtue of being small. It's also decentralized, which is a cool buzzword, but also in practice means that it's nicely broken up into a bunch of small specialized communities in each Mastodon instance that can feel pretty cozy and friendly, way less overwhelming than Twitter.

The really unique thing about it is that it's a weirdo open-source-y alternative social network that actually doesn't appear to be dying off like Diaspora or Voat or Steemit or whatever did - it seems to have reached a sort of social critical mass where people are sticking around because they genuinely enjoy the company and interactions with other users, and is growing at a sustainable rate.