What does it mean when a department has 'retired professors' as part of their faculty? Can I still work with them? What exactly does this mean? Could I do work with them? If not, why are they listed there? I am confused!
Retired (or emeritus) faculty are generally not available as research advisors for graduate students, although depending on the university's and department's policies, a retired faculty member may be able to hire postdocs and other technical staff ("soft-money" positions that can be eliminated if the funding isn't there). 

As for why they're listed: in many cases, retired faculty still retain some active affiliation and involvements with their departments. For instance, they may be involved advising undergraduate students, teaching classes, or continuing to do their own research, but absent a group to work with. (As an undergraduate, there was one chemistry emeritus professor who was still working in the laboratory—at age 80!)