Homebrew is a package manager that makes it easy to install UNIX tools which don't come with OS X. Using the Homebrew package manager provides a great amount of control over the software installed on an OS X system, and it can be used to provide missing elements to run Drupal directly on OS X as a development environment.
I didn't set out to use Homebrew. I simply wanted to use wget instead of curl. I had no idea that would lead me to completely change my development setup.