tl;dr: It installs pre-built binary packages instead of building from source as Homebrew and MacPorts does. There are a few other differences, but that's the biggest one.
To be honest most of Homebrew stuff is "bottled" IE its pre-builts most of the time you no longer have to actually build it from source... So its not even really a difference any more!
Ah, I was unaware - I'm still a MacPorts hold-out myself. (It ain't broke, so I haven't fixed it.) Thanks for the correction.