Frames Per Second
In movie jargon, frames per second is the number of still images that are flashed each second, creating the illusion of motion. In video games, it is the same thing, but there are some minor differences.
The human eye can easily discern the difference in a movie between 24 FPS and fluid motion. While the actual threshold varies, the average human cannot tell the difference between about 75 FPS and fluid motion. In a movie, this isn't a big deal. If you've worked with photography much then you've no doubt seen that if someone is moving when the shutter opens and closes then you will have a blurry picture. In a motion picture that's going to flash still photos at the rate of 24 FPS, the blurred frames actually help the human eye to perceive motion.
In a video game, however, you don't get the blurred frames. Every frame is rendered perfectly to the screen. Due to this difference, 24 FPS in a movie looks a lot clearer than 24FPS in a video game. So the target FPS for a video game in order to create the fullest possible illusion of motion is about 75FPS, which is the threshold at which most humans can no longer perceive the difference between the illusion of motion and actual motion.
Effects and Display affect your FPS rate.
So the ideal FPS in the game is going to be somewhere around 75FPS. After that, extra frames are wasted frames that you can't even see anyway. Many players have found that setting the game to play around 75FPS lets them turn on effects they wouldn't otherwise have on.
FPS and the Older Versions
Since 0.2.7.1, the simulation inside Armagetron Advanced has been separated from the framerate. So the simulation now runs off the system clock completely and there is no framerate-dependent code anywhere in there. In English, that means that higher framerates no longer convey an advantage to players like they used to.
In previous versions, however, there were some pieces of simulation code that were dependent on your framerate, with rubber being the most notorious. So you actually did have a distinct advantage by having a higher framerate than other players.
Wikipedia definition of Frames Per Second
Increasing your fps
There are various ways to improve your fps most of them involving reducing the quality of images represented on your screen. If you go to SYSTEM SETTINGS > DISPLAY SETTINGS > DETAIL SETTINGS / PREFERENCES, you can switch off things like grinding sparks or reduce the quality of images. Explanations are given if you just hover over an option. FIddle about until you are happy.