Hmm... yeah. This one takes more discussion than a simple line or so...
In the progression of video games, they've evolved from 2D games into games that feature 3D graphics. Mind you, the graphics are still displayed on a 2D display device, but internally, the game is composed of three dimensional models in a three dimensional environment. These 3D games were part of what made the original PlayStation so fascinating.
These 3D graphics are, however, eventually shown on a 2D monitor. Your left eye and your right eye see the same image. This image is a flat image. Your mind can perceive that the 2D image is representing a 3D environment and it can extrapolate this data to "fill in the blanks" and, voila! -- you're playing a game in a 3D environment. Even though you acknowledge that the environment of the game is 3D, however, it has a flatness to it, as your eyes see the same image.
The way to give a 3D feel to the game is to show something different to each eye. The reason we can perceive depth of field is because we process visual information from two different views of the same thing. One view is from a slightly different point as the other (the other eye) and the difference between the two images allows us to determine distance away from objects. The trick, then, is to find a way to get different views of the game to each of your eyes.
The EyeFX 3D achieves this feat through two functionalities: LCD Shutters and rapidly oscillating controls injected as controller input. The liquid crystal shutter system alternates between eyes, always having one eye opaque and the other eye clear. This means that you aren't actually seeing the screen with both eyes at any given time. If your eyes aren't seeing the screen at the same time, then your eyes can actually see different images. This effect causes a perceived lessening in brightness and can cause noticeable flicker, depending on your environment. For one setting, that is the end of the story. The fact that your eyes are seeing the screen at different times means that your mind can (under certain conditions) better create a 3D feel. The effect when using the shutters alone is not phenomenal, but can provide an observable - if not measurable - difference in the 3D feel of the game.
The other function of the glasses - injecting alternating inputs rapidly to the PS2 - is what can actually create an honest-to-goodness 3D view in a game. The trick is to select the correct mode so that the EyeFX is sending signals that will shift the view left and right a bit. Depending on the game, this could be by simply stuttering the camera itself left and right, or by actually starting to rotate your character left and right. When the view is changed slightly in this manner, things that are far off near the horizon will move more quickly than things that are closer to the camera. With the shutters synched up with this effect, your left eye will see what it's supposed to and your right eye will see what it's supposed to, creating a true feeling of depth in the game.
The final word? With certain games and the right settings, the effect can be amazing. Nothing seems to come out of the screen, but things will look like they go off deep into the television set. Mainly, this requires a lot of trial and error to find out what games work best.