You say "it doesn't seem to work" so I'm assuming this simple test fails: while in Insert mode enter [ and you should see [|] where | is the cursor. If not then let's look at the installation...
:source in the context of plugins is for vimball files and you would do something like this, once, to install the plugin:
vim someplugin.vba
:source %
:q
(Generally speaking :source just executes the Ex commands in a file.)
But, of course, this plugin is not in a vimball. All you should need to do is copy the file to ~/.vim/plugin/ then start vim. I just did exactly that with the current version of auto-pairs and everything is working fine. (I'm not on Mac, though.) Note that by sourcing it you may even be causing problems that wouldn't normally exist.
If you're using a fairly up-to-date version of Vim you could also try copying the entire plugin directory (including docs\, plugin\, etc.) to the following (create the parent directories if you don't have them already):
~/.vim/pack/bundle/start/auto-pairs
(Note: directory "bundle" can actually be named anything you want.)
Alternatively, if you know git you can clone the whole thing into the start/ directory.
The next time you run vim the plugin will be available. One advantage of this is that you'll have local access to the help file.