With the GPL, you couldn't distribute software that links (at runtime) to GPL software, without open-sourcing your software as well. This is because, linking another piece of software to a GPL'd binary means you're creating a "derived work". That's why they made the LGPL (the "lesser" public license) which allows being linked to from closed-source works, without being considered a derived work.
With AGPL, they seem to have gone the opposite way from LGPL: it seems to have extended the definition of "derived work" to include software that accesses the covered software over the network. If that's the case, doesn't that mean you just plain can't use MongoDB in the backend your own closed-source website (without open-sourcing your site's code?)