Perspective distortion occurs when there appears an unusually or disproportionately large part or portion of your subject relative to its remaining parts when shooting a portrait using a wide angle lens at extremely short focal lengths. In this first sample I've posted, you may notice that the head is out of proportion vis-a-vis the entire body which appeared smaller and tapering down in size. The reason for this is that I used a 24mm focal length on my zoom (or in 35mm language, equivalent to 36mm based on Nikon D50's 1.5 crop factor) and I was very near the subject standing right in front of her with my camera slightly above her head.
This kind of distortion is dependent on the distance of the camera in relation to the subject you are shooting wherein the nearer you are as photographer to your subject or model, the greater this distortion would be. Some refer to this as a wide angle distortion which is also accurate in the sense that, you can only get this kind of distortion when you use a wide angle lens. Perspective distortion is often pleasant in landscape photos as they give a wider view of a scene but doesn't hold true in portraits where the nose appears relatively bigger as compared to any part of the face or head which is farther away in distance from the lens. There are instances when perspective distortion even enhances a portrait but most often than not, it ruins what otherwise would be a great portrait.
When shooting portraits, it is therefore recommended to use a short to moderate telephoto lenses with a focal length of 50mm to 125mm. If what is attached to your camera is a wide zoom, you can minimized this distortion on your portraits by moving back away from your subject, thus creating instead a pleasant environmental portrait with any conceivable background of your choice very much seen on the frame.