Why are tractor trailers’ (trucks) referred to as semi’s? Exactly what are they half of?
They are semi-articulated.
They can’t really talk proper you see 
They’re half of a trailer. A semi-trailer only has wheels near the back, and part of it’s weight is resting on the back of the tractor.
In Australia, our interpretation of the term “semitrailer” is that of the complete unit: truck plus trailer. We refer to the truck on its own as the prime-mover. I think Americans refer to it as a tractor.