Tenon and dovetail saws cut on the push stroke, so the spine acts as a support to keep the blade stiff and stop it from bending as it moves through the material.
This also allows the saw to make perfectly straight cuts.
As well as this, the spine adds weight to the saw, meaning less downward pressure is needed from the user when working.
Please note: If the spine is wider than the blade, it limits the depth to which the saw can cut.