Keeping the torso upright loads the triceps, while tilting forward shifts the load onto your pectorals.
This occurs because you always perform work against gravity on the vertical axis. By keeping totally upright (and thus parallel to the vertical), your pecs aren't being subjected to as much load since they are mostly activated during pressing movements. As you tilt forward (away from the vertical), you begin pressing with your chest.
If you were to tilt to the extreme, your body would be parallel to the ground. In this case, you'd essentially be performing a mid-air pushup, unsupported at the feet.