It doesn't.
AGPL means the only people using it have to licensed the same.
AGPL means the only people using it have to licensed the same.
AGPL only requires open sourcing any modifications you make to the software when you give users direct access to a server running the software, which seems like something you would never want to do in case of a database.
You can use database servers running AGPL software in a closed source SaaS: http://www.gnu.org/licenses/why-affero-gpl.en.html