One of the biggest problems with Google+ has been its inability to create a group wherein all peers are equal. You can create a hashtag that everyone can post to but you can't control the membership of, or a Page that a few moderators can share to, but it's difficult to add users to (for non-public posts, Pages can only add users to circles once they add the Page first). Communities finally fixes this problem by creating public or private groups that anyone within can share to.
The Communities feature includes everything you would expect from a separate group: you can submit public posts that everyone can see, or just private posts that only members can access. You can initiate Hangouts just for your group and schedule Events that only they can access. Most importantly of all, though, it creates a permanent home for the whole group. Pages just haven't quite been able to cut it in the past. This is a wonderful, welcome addition.
Google is calling this a "preview" right now, so it's unclear if everyone will have the full functionality from the start, or if it will rollout to select organizations and users first as with things like Hangouts on Air. It's also only available on the web. Mobile is "coming soon."
Source: Google Blog