I was at my club, looked up at the ceiling and noticed that the ceiling, floor structure is a series of 4x4 molds that are poured on. The mold is set, mouth side down, 4x4 foot pattern and gives beams that arou probably less than 6" wide and floor thickness probably around 3". Steel runs in the beam section of the molds. I know this is hard to explain, but can anyone identify this for me? concrete nut

If your dimensions are in feet rather than inches then it would apear to be a two way joist system. They have been around for many many years. Used mostly in commercial buildings for large open spans and high loading conditions.
Regards,
Joe

Hi concretenut:

Jredburn has pretty much summed it up -- I just wanted to add this would also be called a waffle slab, often used with the so called flat slab construction. And as Joe said what you described was a two way joist type construction, and of course there are cases of pan type constrction with oneway joists as well.