Most lenses are “rectilinear,” which means they’re designed to project an image onto a flat surface (the film or the image sensor) and render straight parallel lines as straight parallel lines. This is actually a complicated optical trick, since a simple lens really wants to project an image onto a spherical surface (such as the interior of the human eyeball). It also becomes increasingly complicated to do as the field of view of the lens becomes larger, as with wide-angle lenses - one reason why really wide angle lenses are so expensive.

This type of projection onto a flat field is something that different lenses do to varying degrees of success. High quality lenses, particularly those intended for use for macro or architectural photography, do a pretty good job. But cheaper lenses will compromise on this slightly and will either barrel or pincushion somewhat. That is to say, a photograph of a square object may appear to be either bulging outwards or squashed inwards, because parallel lines are being portrayed as curved. In fact, nearly all cheap lenses tend to have barrel distortion - it’s just that people usually don’t realize it because they rarely take photos of square or rectangular objects.

Obviously any lens can be used to take a portrait of someone. However, the results can be very different depending on its focal length.

The distance required between you and your subject, when you take a head and shoulders portrait, depends on the focal length of the lens. If you have a wide angle lens then you need to stand very close to them in order to have their head and shoulders fill the frame. But if you have a telephoto lens then you need to stand a fair distance away from them for the same effect.