Teams allow you to share groups with specific subsets of your users (you can read more about teams and how to create them here). Here are some tips and three examples to help you structure your teams.
Teams within your company
If you think about how your company is structured, you might find some obvious teams. You could create teams of your users based on their role at the company -- here at Less Annoying CRM, we have a team for our CRM Coaches and a team for our developers. Do you have some people in the office and some people in the field? Do some employees handle different geographic areas or certain kinds of clients? Creating teams will allow everyone to focus on the groups that matter to them and filter out the rest.
Completing a special project
Teams can also be helpful for keeping groups related to a specific project from cluttering your CRM. Imagine that your company is planning a special customer appreciation event in several months, and a couple of people are in charge of coordinating it. The planning process will involve several different groups of contacts -- customers to invite, VIPs, potential speakers, etc. Only the people in charge of planning the event will need to work with these groups. By putting those two into a team, they can create all the groups they need without them showing up for all of your users.
Delegating collaborative work
You can use teams to delegate collaborative work. Let's say that you have several salespeople and you just got a long list of new leads. Rather than assigning leads to each individual, you want your salespeople to pair up and reach out to sections of the list together. You could create those pairs as teams and create groups of the new leads to share with each team. Your teams could treat these groups like shared contact assignments and work through them collaboratively.