When your Groups are ready to be used, you can choose them as recipients to target contacts included in these Groups when sending an email or SMS. You can select one or several if you want to refine the targeting.
Go to the sending interface for email or SMS, then in the Recipients section, check the Group(s) you want to use and click the right arrow to move them to the right side: 
Your recipient will already be updated when you send the message, as long as the contacts' data are updated. This way, you won't have to manage a recipient list manually.