An Eloqua Email Group is not a list of contacts, rather it is an email content category. WHAT you are sending out, not to whom.  It is a group of similar content that your contacts can unsubscribe from. 

Think of an Email Group as you would a subscription to National Geographic magazine you have mailed to your home on a regular basis. If you subscribe to many different magazines (general topics within), you can stop receiving that magazine (topic category) by ending the subscription. 

In Eloqua, a contact could click "unsubscribe" in the email footer and that would stop the contact from receiving any Email asset designated with that Email Group.  

Here is an example of a set of Email Groups a departmental account may use:

The audience for the email content is handled independently via Shared Lists and/or Segments (you use these to send your email via a campaign).  

Only UW-Madison Eloqua Administrators can create Email Groups.  This is normally done in the departmental onboarding process, though new Email Groups can be requested as needed.