It's a website that allows you to race games with other speedrunners. How it works I'm not sure because I don't use it :(
There are a couple parts to SpeedRunsLive (SRL). The first is the front page and the second is the racing system. The front page is fairly straight forward, if you have I think like an hour of race time, you get your stream put on the front page when you connect it to your SRL account.
As for the racing system, it's all done via IRC and a program called RaceBot. It's fairly straightforward, especially if you have the slightest understanding of IRC, and there are guides on the website itself on how to use RaceBot. But once you register a nickname on the SRL IRC server, you can join and start races as you please on the site.
That's really all there is to it, nothing too overly complicated, although the IRC can trip people up at first.