What more does installing Homebrew allow me to do?
HomeBrew is a package manager for mac. It facilitates the installation of different tools by installing and configuring all dependencies as well as the program itself.

You can think of it like the Mac App Store for unix apps. If you are familiar with Linux, then Homebrew is exactly like the Linux package manager. For a complete list of everything you can install go here : https://github.com/mxcl/homebrew/tree/master/Library/Formula/

If you don't know what you would need it for, then you probably don't really need it.