The AGPL license is a variant of the GPL license with a broader view on distribution of the software. The main difference between GPL and AGPL is that the latter also considers accessing an application remotely as distributing it.
The core precepts of the GPL (and AGPL) are
- If you distribute an application, you must also distribute the source code
- Even if only part of the application is copyrighted under (A)GPL, the first point applies to every part of the application.
This means that, if your modules interact with ownCloud or otherwise form a single 'application' with it, then you must release your modules under the AGPL license as well (or a license that gives them at least as much rights on the source code) and you must provide access to the sources of your modules.
It might be possible to create a successful commercial app based on it, but you won't be able to compete on features. So, you will need other attractors for subscriptions, such as superior content, customer service, etc. Whether that is achievable can only you decide.