Groups allow users to categorize their contacts. You can create a group when importing contacts or add the group later and designated contacts as needed.
Ex: I am importing a file of contacts from company ABC, I create a groups ABC upon import to keep the company contacts together.
Creating groups also allows account owners to send campaigns to contacts.
Ex: I want to send an email campaign to all of my contacts who are prospects, as they will require different information than an existing customer.
You can have the same customer in multiple groups if needed.
Ex: I have a new customer that is interested in News Letters and promotional updates. I will add this customer to my Existing Customer group and my Promo Interest group.