Back in the days of camera reels directors of photography toyed around with idea of framerates and figured out cheapest possible way to manufacture, tape and produce movies and tv shows. At the time it was determined that 24fps was a decent alternative to having to pay for reel after reel after reel. As a result for over 90 years 24fps became the industry standard. In recent years movie producers started using digital formats such as red eye technology which shoots a bunch of images... some huge number like a 1000fps. Human eye will not really notice the difference at certain point but shooting at higher frame rate has a lot of benefits.
If action happens too fast on camera... footage comes out to be a blur. In other words when an object on the screen moves from somewhere to somewhere he, she or it generates motion blur. Shooting at higher frame rate reduces that blur. For normal moving things (ie a person walking or running) higher frame rate is of little significance. For fast moving things (ie a car crash test, mountain biking, car racing etc) it becomes paramount to capture stuff in higher frame rate. Reverse comes out to be quite awkward. If you use high frame rate on a slow moving target it will appear that target is moving too fast and that is why many people reported seeing Hobbit as it was on steroids especially first 15 minutes.
Best real life example of how high frame rate works is as follows:
If you were to take 1 picture per second for 60 seconds and export that to a video at 30fps while coding each picture to appear at predetermined time interval... you would barely get 2 seconds of video as your result.
120fps effectively captures almost 4 times amount of images per second than traditional 29.9fps format. You can slow down footage by 50% or by 75% to show objects in slow motion. Hypothetically you can keep slowing it down and down but at some point it will be redundant and video will appear pixelated and of crappy. There are software packages like Twixter which multiply framerate slowing it down to like 1000fps in super slow mo (check out many youtube videos on that topic).
For scuba diving coming from personal experience... I winded and complained about 30fps video capture and was thrilled when 60fps came out a few years ago. Now that 120fps is here I have yet to test it in scuba environment but I know for mountain biking it works wonders by reducing blur by about 50% as it appears to naked eye. Huge improvement if you ask me.