What does GitHub for Windows' "sync" do?
Sync does git pull --rebase and then if there are local changes, it does git push.
From here: http://haacked.com/archive/2012/05/21/introducing-github-for-windows.aspx#87318
Since the above answer was more than two years ago, an updated answer to this question is: due to some bugs with rebase, the "sync" button does not do git pull --rebase anymore. Instead, it does git pull which will do merge if there are conflicts, according to this release notes (see release 1.3.0).
The link above is not available at this time. Here is the new release notes.
"Sync" would be any actions necessary to have your local branch match your remote branch. If your local branch had commits that your remote branch didn't, then "sync" would push your branch. If the remote branch was ahead of your local branch, then "sync" would pull first (specifically, git pull --rebase, as was explained by Phil Haack). "Sync" is just a shortcut to getting the local and remote to mirror each other.
From the GitHub site:
The sync button turns the complex workflow of pulling and pushing into a single operation. It notifies you when there are new changes to pull down and lets you quickly share local changes.