Higher energy electrons can knock out electrons which are more tightly bound to atoms.
Other electrons fall back into the vacant energy level and emit an X photon.
Another way intensity can increase is when the current from the cathode has not reached saturation.
Then the increased PD drags more electrons away from the cathode, and they reach the anode quicker because they are moving faster. So there are more X photons generated per second.
@Abcd So there are 2 ways in which increased PD can increase intensity of X rays : (1) increase in energy of each X photon emitted, (2) increase in the number of photons emitted per second.