Let's say you're building a website, and you want to add two new features to your site. A forum and a chat room. You're working on both, and then a critical bug comes through that you need to fix. What do you do with the forum and chat room code you were working on?
If you're using Git, you'd have a branching model, and any new tasks would be in their own branches. Also, the live branch would be separate from your main development branches. You'd have separate branches for the live site to fix critical bugs (with their own branches, of course), a forum branch and a chat branch.
This, for me, is the biggest benefit of source control. Keeping your source code safe is obvious, but this has been around for years with SVN and numerous other source control tools. Only since distributed version control tools have become mainstream has branching been considered a first-class citizen, and absolutely necessary to building a website.