Lens distortion can be a combination of different factors, and nearly every lens has it. Cheap lenses can have some amount of Chromatic Abberation, which is a purple haze that appears around very bright edges of a highlight. Zoom lenses are also prone to barell distortion, which is the bubble or pincushion effect you see at different zoom lengths. Normally you don't notice any geometric distortion until you take a photo that has straight horizontal or vertical lines, such as a building, a doorway, or even a product box.
Even if you have an excellent lens with little distortion, you may take a photo where the perspective isn't quite right. You may have intended to get a forward shot of a sign a few feet above you, but unless you have a ladder you'll never be able to get a straight shot at it.