Frames per second or FPS in simple terms are how many images per second that get refreshed back as a video.

Higher frames per second appears smoother because it catches more. Higher can mean anything as 60fps is fine but for slow motion 120 or 240 fps makes the footage really smooth when  slowed down because it is capturing more “images”. ^{Wikipedia frame rate}

More frames means more information

Do note that the more frames per second means more file size as you are capturing more information.

In the image below 0 = a frame. This gives a good visual on how many frames you capture per second depending on the setting.

Now an example clip, first at 60fps then at 50% speed which is 30fps. 40% gives 24fps and 20% gives 12. The equation for this is done like: 100/40 = 2.5 then 60/2.5 = 24

Here are the examples note that slowest isn’t always the best as 12fps looks a touch choppy whilst 24fps looks very smooth.

Examples

60fps:

30fps:

24fps:

12fps:

It’s often hyped around YouTube videographers that 24fps give the real “cinematic feel” that’s purely just personal opinion there is no such science behind it. In most cases its cited as that is what films and movies are shot in to give a more real life look.