Groups allow you to organize your teams by departments, squads, functions, skills and whatever else you see fit. Once a group is created and members have been added to it, you can assign groups to cards and mention them just like with any other member. You can also share collections to groups and filter by them in the member criteria in reports.
Unless restricted, any member or administrator in the organization can create groups and you access the dialog right from the top-right toolbar.
Once a group has been created, group owners and administrators can easily add and remove members; change member roles within the group; edit details, such as the group name and logo; or delete the group if it is no longer needed. A group is treated just like a member when it comes to assignments and mentions and is a great way of communicating something important to a whole team at once. You can read more about communicating in Favro here.
If you are working in a growing organization, it is a good idea to get into the habit of setting up groups early to make collection sharing a streamlined process. Have a new product team joining? Add them to a group and share them the collections they need access to with a few simple clicks.
Now that you have your teams divided by group, you might be interested in reading about some best practices when it comes to organizing collections.