The point is to bring better visibility to group suggestions and at the same time give better control to (the owners of the content, visitors and group administrators).
A. You now have the choice between:
- forbid group suggestions in your space: in this case the "suggest a group" button  will not be displayed in your space for your visitors
- allow your visitors to suggest groups to you but only yourself is aware of these suggestions. 
- allow your visitors to suggest groups to you and make these suggestions visible to your visitors  - DEFAULT CHOICE
For this go on the bottom of the page : Account settings / Photos and other content. 
B. You can suggest groups which you are administrator/moderator of but also - and this is the new feature- ALL GROUPS YOU ARE A MEMBER OF 
to a few exceptions below
C. The group administrators can reserve the right (and to the moderators) to suggest content in their groups. This alteration is done on the administration page of the group / Limits and Moderation .
D. Private groups cannot be suggested.