First, you won't see the group on your list. When you click on your Facebook groups, you will no longer see the group you left on your list. This is helpful if you want to focus on the groups you do care about, as there will be less visual clutter once you leave unwanted groups. Second, you won't receive notifications. Essentially, leaving a Facebook group is just like unfriending someone—you will no longer see group posts or receive activity notifications.