Barrel distortion and pincushioning are terms you will hear to describe the ability of a given lens to control image distortion. The less you have of these, the better your digital SLR lens usually is. If a lens is prone to distortion, buildings will lean to the center of your photo, horizons may bulge, and faces will appear out of proportion. The wider the focal length of the lens, the more prone it will be to distortion.
In order to overcome distortion, manufacturers add extra lens elements to try to counteract the effects. However, the success of such a technique does vary from lens to lens. So, read lots of reviews on your chosen lens, and try it out if possible, in order to minimize distortion in your photos. Zero distortion is rare, especially in wide-angle zooms, but you need not worry about that. Many digital photo editors are more than capable of correcting this in post processing.
Of course, the exception to this effect is the fisheye lens. When you use a fisheye lens, you are deliberately distorting a given scene in order to achieve a specific photographic composition.