As Reese says in the first Terminator film:
These were different. Sweat, bad breath, everything. Very hard to spot.
So, the living tissue must have something like normal biological processes, right down to having sweat glands and hosting bacteria to cause bad breath.
In addition, we see in Terminator Genisys that
the Terminator's living tissue can survive for decades, aging as if it were normal human flesh; and it can regrow flesh after it has been stripped away from the metal skeleton, although for something the size of an arm the process takes years.
It seems unlikely that the Terminator has enough onboard nutrients to sustain and regrow its flesh in this way. So, it must be able to absorb nutrition from food, which would imply some sort of rudimentary digestive system. Possibly the food has to be of a special type -- perhaps it requires a liquid nutrient solution, similar to that used for intravenous feeding.
It would also need an equivalent of lungs, as well as a circulatory system. We don't see injured Terminators bleed much, but this might be explained by a very efficient clotting process.