OwnCast is sort of the Fediverse’s alternative to Twitch, and lets people set up their own independent live streaming servers which form part of the Fediverse. People can follow OwnCast accounts from Mastodon etc. and they’ll see a post in their timeline when the stream goes live.
To discover streamers, there’s an official directory of streamers ⧉, there’s a bot you can follow ⧉ which posts about new streamers, and you can follow FediVideos ⧉ which boosts interesting streams (as well as other kinds of videos on the Fediverse).
If you want to try following a stream from Mastodon etc, click on the stream’s Follow button (the one with the rainbow Fediverse logo on it). This button is usually just below the video window in the desktop view. Alternatively, you may see people mentioning a stream in posts, and clicking on the mention will bring up its profile including a follow button.
OwnCast runs on free open source software, so anyone is allowed to set up their own server. You will need a bit of technical knowledge to do this, but there are various options to make it easier explained at the quickstart guide ⧉.