How does U-Verse work? Cable? Phone line?

Most likley it's running on the copper cabling to your home.  Some new houses have fiber to the house so if yours is new it could be fiber.  You would know if it's fiber because the installer would have installed a battery back-up of some sort to feed the fiber box outside with power.

Uverse is IPTV (Internet Protocol Television), which is delivered to your home in four streams of internet packets.  The packets are then sent to the stbs in your home where they are decoded and displayed on your televisions.  The RG (Residential Gateway) is what receives the services from the outside world and brings them in to your home.  The cables used to connect the RG to your STBs (Set Top Boxes) can either be coax, Cat5, or a combination of the two.  If you need more info I'm sure someone else will be along to add more info to this explanation.  Welcome to Uverse.

 simply put the tech told me the services are ran on the phone lines from a point to the house then converted to either coax, cat-3 or 5 inside the home ...  makes sense ??

Amen, FTJ.  That's pretty much exactly how our home is set up.  The fiber optic cable feeds the big VRAD box somewhere in the neighborhood......in our case about 2100 ft. away from our house.....then from that box the signal is carried on phone line to the house.  In our installation coax takes over at the house entry point (the NID) and the rest of our system is via coax to the residential gateway (RG) and from the RG to two of our TV's.  The RG is in our computer room so the desktop is fed via ethernet cable and so is the 3rd TV which is located in that room.  Kind of a wild mixture but it works.....very well in our case.