Contacts can be assigned to groups. A contact can be assigned to a group at the time of creation or afterwards. A contact can only be assigned to an existing group. If no group is specified, the contact is listed as "Unfiled." Unfiled is not literally a group but a statement about the contact's group status.
To assign a contact to a group at creation, select the desired group from the "Group" drop-down menu as you are filling in the fields on the contact editing page.
To assign an existing contact to a group, please see "Copying and moving contacts."