AGPL is a copyleft license. Copyleft gives every person who receives a copy of a work permission to reproduce, adapt or distribute the work as long as any resulting copies or adaptations are also bound by the same copyleft licensing scheme. 

A commercial license allows usage of the work per the terms of the commercial license agreement, without the copyleft requirements (i.e. users are not required to open source their application as long as they are compliant with the terms of the commercial license.)