What is "distorting wide angle for a medium shot"?

A medium shot refers to a shot taken from a "medium-distance", although not a quantifiable one. In film, they are usually used to capture at least half of a person's body within a frame, or even a small group of people. The camera isn't too far to capture the entire setting (long shot) or too close to a person's face (close-up). Here's an example:

A wide angle lens is self-explanatory: it squeezes an indefinite amount of the surrounding into a limited frame. Here's an example (note how it's similar to a rotational panorama):

And with the two combined, you get something like this:

The wide angle is "distorting". The medium-shot brings the focus onto the situation - the surrounding settings with the character in the center. Together, they can highlight a dazed character in a "weird, slightly off-kilter world", just as Shyamalan intended in Signs.

It might be clearer to read the quote like so:

And once again he uses camera tricks - like the distorting effect that wide angle lenses have on medium shots - to create a weird, slightly off-kilter world.

The effect they are describing is the result of decisions made regarding:

1. a camera lenses angle, and
2. the proximity of the camera to the subject.

Lens angle change from a fixed position:

Wide angle lenses are often used for close-ups or "detail" shots with little mid- and background in the shot. Given the close proximity of camera and subject, the resulting "detail" or "extreme close-up" image does not appear distorted.

Here's an example of how lens angle affects the image in a medium shot:

...were this camera instead close enough for a detail of the subjects nose, the distortion would not be as apparent.

Using such a wide angle lens for a medium shot (head/shoulder to head to toe) or a "wide" (or "long") shot where the mid- and background is in frame makes the whole shot look distorted. The "wider" the lens angle, the "deeper" or more "fisheye" the image; the narrower or "longer" the lens angle, the "flatter" the image.

To keep the perspective from looking distorted, the proximity of the camera to the subject needs to be altered, e.g.

Combining simultaneous shifts in the two, i.e. a change in camera proximity to subject while shifting between a wide angle lens and long lens, results in the "dolly zoom" effect. This dolly zoom shot from "Jaws" clearly demonstrates the differences of image distortion when altering camera proximity to subject and lens angle: