I want to develop a piece of software that other developers can use in their projects. It has to be active at runtime however, and perform some standard functionality every time the application runs. It is essentially software that provides extra functionality to the application developer and its users...

I'm not sure how I might do this, and my google-fu has not been strong enough to find a definite answer.

A little light on details but here's a trick I used long ago. To make a service available to just about any language app I set it up as a miniature server or service. You would connect to it via IP, send your query string much like SQL and the answer would come back on the same pipe.

Whether this applies or not is something I can't guess given what has been revealed so far.

How about something to manage Users... logon, password verification, privileges/authorisations, preferences etc
You could have it as a API then optionally layer a GUI on top.