A portrait lens is any lens with a focal length between 80-135mm (for a 35mm camera). This allows portraits to be taken with a slightly flattened perspective, flattering the subject's features and improving the aesthetics of their face (a wider lens will make their nose/ears look huge, a longer lens makes the face look unnaturally flat).
Because of the demands of the fashion industry, portrait lenses are often amongst the fastest, sharpest lenses in a manufacturers lineup, but because of their simple design they are relatively cheap. Their versatility extends beyond portraiture. These lenses are also short telephoto lenses, and will probably be faster, sharper smaller and lighter than a 70-200mm zoom costing twice as much.