Favorite groups are a way of personally organizing posts. How you use them is up to you, some examples are for the absolute best out of your favorites, comics you plan to read, posts you intend to translate, or something too subjective for a tag or a pool.
Favorite groups function similarly to pools in that they are an ordered collection of posts that can be browsed through. The main difference is that the creator of the favorite group is the only one who can add or remove posts from it (though anyone can view the posts in it).
Viewing your favorite groups
Your favorite groups are listed under "Fav groups" in the menu on the main /posts page, and under Statistics in your user profile.
Adding a post to a favorite group
Click the "Add to favorite group" link in the sidebar, then select which group to add the post to (if you only have one group, you won't have to select which group to add to).
A shortcut is to press the "g" key to open the "Add to favorite group" dialog, then press a number key (1-9) to select a favorite group.
Removing a post from a favorite group
You may also edit the favgroup to remove posts from it. To edit a favgroup, go to the main Posts page, click "Fav groups" at the top, click on the favgroup in the list, then click "Edit" at the top of the page.
Favgroups are public by default. You can make a favgroup private by editing the favgroup. To edit a favgroup, go to the main Posts page, click "Fav groups" at the top, click on the favgroup in the list, then click "Edit" at the top of the page. Uncheck the "Is public" box to make the favgroup private.
Basic members can create up to 3 favorite groups, Gold members can create up to 5, and Platinum members can create up to 10. A single favorite group can have up to 10,000 posts. See help:users.