Groups can be used as mailing lists, discussion forums, and to easily share items with specific groups of colleagues and/or students. You can send email and email attachments to groups. You can also share google docs, calendars, sites, folders with a google group instead of individuals.  You can adjust your group settings to receive each message by itself or as one daily digest. Messages sent to groups are archived and do not expire, allowing users to easily search and view past and present discussions via the web interface. Group members can access and search archives of mail sent to their lists to efficiently find past discussions or shared documents. 

Google Groups vs. contact groups
You might be wondering how Google Groups differ from the contact groups you can create in your contacts. The primary difference is that a Google Group has its own email address, so anyone in the group can send messages to it. Your contact groups, on the other hand, are for your personal use, and they don't have their own email address, so no one else can send messages to them.