I would imagine it would be a set of APIs a website could use for new user signup, logging in, session tokens, logging out, and retrieval of lists of users based on some criteria.

This could be a hosted solution or one that you install on your own servers (preferably self-installed and easily modifiable) - either way you'd set it up, code your own visual interface for logging in, signing up, etc, but use the user management API on the back end for storing user data, storing new user data, etc. It would also utilize smart encryption techniques, allow for mass emails, etc.

I understand that these issues are mostly straightforward, but it seems crazy that every new web app has to re-invent the wheel for user management!?