35 mm Film
Kurosawa was known to be a director deeply involved in all aspects of production, including doing his own editing. The mode of production was pretty typical for the time: 35 mm film, shot with several cameras to pick up the action from multiple angles. That shouldn't surprise anyone. The surprise was Kurosawa's use of a telephoto lens, which achieved a technique known as deep focus. Together with the camera placement, it informed the action in a unique and extremely innovative way.
As a technique, deep focus creates multiple planes of action, where one thing can happen in the foreground, another thing in the background behind it and a third thing in the way background behind it. That means he can set up numerous complicated shots and get it all to work, which is why those fight scenes have that dynamic, action-packed element to it (all without the use of a single computer-generated image). He was a master in the use of movement in his shots.
Combine that with the camera work and you start to see why later movie directors go so gaga about it. Kurosawa didn't have sophisticated matching techniques at his disposal: no way to shoot a scene out of sequence over several different days, then assemble them together into a coherent whole. Hollywood does it all the time, but it takes careful planning and a lot of hard work to ensure the shots match.
Instead, Kurosawa set up multiple cameras to cover the action scenes and just let 'er rip. One camera was the "main" camera; one camera was set up elsewhere to pick up fast shots; and one camera just sort of picked up what it could. Kurosawa would plan out their movements before the shot and coordinate them with those of the camera.
It was frenetic and chaotic, but because multiple cameras caught the same action, he could then assemble it with confidence and ensure that the images all matched. That gives the film part of its energy, and in fact the whole thing worked so well that Kurosawa repeated the technique for a lot of his movies going forward. Other filmmakers saw what he was doing and emulated it in their own movies. (Don't believe us? Check out this behind-the-scenes clip from Indiana Jones and the Temple of Doom, where Big Daddy Spielberg talks about the multiple cameras required to catch the collapsing bridge scene in the finale.) Thus was Kurosawa's style woven into the fabric of the medium, and the technical aspects of his production turned into something that a whole ton of influential directors wanted to use themselves.
One shot that you've seen in zillions of films is one that Kurosawa did first in Seven Samurai—the horizon shot. That's when hordes of Roman soldiers or bandits (in Seven Samurai) or good guys on horseback or aliens or Nazis or whoever appear en masse coming over the top of a hill or from somewhere else on the horizon in the far distance and move slowly towards the foreground. Here's a Spielberg take on it from Close Encounters of the Third Kind. That shot, and countless others, are movie tropes by now, but they had to start with someone.
Someone who will not be mentioned but whose initials are Akira Freaking Kurosawa.