The big difference between watching and starring a project comes down to notifications.
If you are watching a repository, you will receive notifications for all discussions — project issues, pull requests, comments on commits and any other comments. If you’re not watching a repo you’ll just receive notification for the discussions you participate in.
On the other hand, if you star a repository, you basically want to show your appreciation as well as keep track of repositories that you find interesting without it spamming your timeline.
This is clearly stated here in the Github blog post,
A quick note: activity from starred repositories will not show up in your dashboard feed.
The other main thing worth noting is that any repositories you were previously watching can now be found on your stars page. If you want to go back to watching them, you’ll need to change them over yourself. There’s also a new auto-watch feature; when you’re given push access to a repository GitHub automatically adds it to your watch list.
You can see a list of your starred repos at github.com/stars.
And popular starred repos at github.com/popular/starred