What academic functions does a Professor Emeritus usually serve? I for one have never understood the distinction between a regular prof with a prof Emeritus/Emerita aside from the obvious fact that a Prof. Emeritus is someone who is usually fairly elderly and has spent quite a bit of time in the University.

I am currently spending a working with a Prof. Emeritus who is the a supervisor/advisor to my project and conducts biweekly meetings (which are really brief chats about life) and am in need to make a serious request. I feel uncomfortable because he may have a lot of other work on the side. I do not know whether has classes on the side nor am I aware of any research activities.

How does a professor become Prof. Emeritus (is age-status a must?) and do Prof. Emeritus usually still actively conduct research, teach classes? What is the distinction between a retired professor and a Prof. Emeritus?
To the best of my understanding, the primary function of a professor switching to emeritus status is that it frees up a faculty slot for a new hire.  Emeritus is essentially retirement without giving up affiliation. An emeritus professor can ramp down their duties, go part time, etc.  In some cases they may still do some teaching and supervising, and may have office space, but I believe they are typically no longer paid and no longer expected to fulfill normal faculty duties.  That said, when they are still active, their advice and participation is often still quite valued by the active faculty.