TRAM stands for Transverse Rectus Abdominus Muscle, a muscle in the lower abdomen, between the pubic bone and the waist. Tissue (skin, fat and muscle) is taken from the lower abdomen, slid up through a tunnel under the skin to the chest area, and formed into a natural looking breast. A second, minor surgery is needed to reconstruct the nipple and areola.
In a traditional TRAM flap procedure, the moved tissue remains attached to its original site. The blood vessels are not cut, so the tissue retains its own blood supply.
In a free TRAM flap procedure, the tissue is completely removed from the abdomen and transplanted to the chest. The blood vessels are cut and then reattached to blood vessels in the chest area using microsurgery techniques.
Removing tissue from the abdomen means you end up with a "tummy tuck" (a smaller, flatter midsection) which many women see as an advantage to this surgery. On the other hand, if you're thin and don't have enough excess abdominal tissue, the TRAM may not be appropriate for you.
A reconstructed breast that uses abdominal tissue feels more like a natural breast to anyone touching it, though the reconstructed breast will have little or no sensation for you. The surgery does leave a scar on the abdomen and removing the muscle weakens the abdomen (at least at first; eventually you should recover full strength).
Tissue can be taken from your abdomen only once. If you ever need a second breast reconstruction, the tissue used will come from elsewhere, such as your back.