Hi! I'm not sure if this is the right place to ask this, but this has been bugging me since I've seen it. I haven't heard much of this in older martial arts movies but I have in newer movies.
This is called a Kiai, a shout done during a move to startle your opponent, as well as teach you proper breathing technique during kicks especially, where you want your diaphragm and stomach muscles to be taut so you can direct moves properly.
In Japanese martial arts such as judo and aikido, which I've taken before, it's "Ai-yah" instead, but really, the idea is the same.
Source
Forrest E. Morgan, Living the Martial Way: A Manual for the Way a Modern Warrior Should Think, 1992