When you include an AGPL library your program becomes a derivative work, so the rest of your program becomes AGPL-licensed as well. The boundaries of what part of the system should or should not be included are vague, because *GPL licenses are written with C semantics in mind. So, while having a library directly in the same running process definitely makes you work a derivative, it's not clear if you the same is true if the library is a part of a different process and your program talks to it via an IPC, a filesystem, a database, an API, etc. Depending of the interpretation you may have toped-source just a tiny part of your program running on a server, or all server-side and client-side code and all supplemental scripts, tools, etc. needed for the system to run.
So, it's legally ambiguous, and since no-one has legally tested the waters the interpretation of the license can be very different, but most people prefer to stay away from AGPL code altogether.
So, it's legally ambiguous, and since no-one has legally tested the waters the interpretation of the license can be very different, but most people prefer to stay away from AGPL code altogether.