I hear this term used pretty often. Does it refer to a specific focal length? Or very low F-number? What does a lens need to have in order to be considered "portrait lens"?
Generally speaking a portrait lens is a moderate telephoto (for 35mm film, maybe something in the range of 85mm to 135mm) with a moderately wide aperture (again for 35mm film, f2 or so).
As to why telephoto, a longer lens allows the photographer to fill the frame with the subject's face/shoulders without the apparent distortion of features you would get from being close to the subject with a wide angle lens. Telephoto and a wide aperture also helps reduce depth of field.
Note -- it isn't unheard of to use 180mm and 200mm lenses (35mm film) to take portraits, this tends to flatten the features a bit which can be an agreeable effect.
The lenses I see most often used for "portraits" (and by that I mean traditional ones without wacky dramatic wide angle effects) are 85mm prime, 100mm prime, and 70-200mm zoom. Fast lenses do often work better, but it's a two-edged blade: You have to nail your focus if you open up, so watch for that. Additionally, if you are used to a moderately-wide to somewhat-telephoto like a 24-105mm or something like that, you'll need to get used to the amount of room it takes to shoot with a telephoto.
The term "portrait lens" doesn't explicitly define a specific type of lens. That is, lenses aren't generally listed as "portrait lenses". Rather, portrait lenses are a subgroup of lenses that all have and produce desirable characteristics when used for shooting portraiture.
As others have mentioned, most lenses that fall into the "portrait" category have wide apertures and are in the mid-focal range (24-105mm) (though it isn't uncommon to use telephoto lenses from further away and zooming in). Beyond that, what a lens can produce is really just at the mercy of the photographer's own creativity.
It all depends on what you're attempting to achieve in a portrait. Prime lenses (fixed-focal length) with a low F-number (wider aperture) are fantastic for head shots and mid-shots (I call them busts...mid-chest and up). Telephotos are great for full body shots (further away from the subject, zooming in).
There are a wide array of affordable lenses for portrait photography, with the most popular and affordable being the "Nifty 50" that some have mentioned and is a favorite around here. It's about a $120 lens that is 50mm f1.8 which will allow for fantastic depth-of-field for closeups and busts. If you're looking into getting into portraiture, this is a phenomenal lens to start with.
Just about any lens can be used as a portrait lens, but the attributes you typically look for include:
- [ed] Normal to near-tele focal lengths (depending on crop factor) - this helps people appear similar in shape and proportion to the way we see them.
- Good bokeh - this helps separate subject from background.
- Clarity and sharpness - although some photographers prefer a soft-focus look, it's always nice to have the ability to control that deliberately, rather than having it as a lens "feature".
These attributes make prime lenses popular candidates for portraits. As long as you're controlling the setting of your shot and you don't need to switch focal lengths rapidly, you don't need the flexibility of a zoom lens, and it's tough to beat the optical speed and sharpness of a prime lens (especially if you factor in budget).
My personal favourite is a Sigma 28-105mm f2.8 easy to use and with short depth of field for snappy portraits.
On a technical point there's also a payoff between lens length, subject distortion, and the room required to work in.
A short lens used close to the subject can produce a distorted 'big nosed' image. A long lens will produce a flatter image but at the expense of needing to be a long way from the subject thanks to the minimum focus distance and so needing more room to work in.
This is why I like the 28-105 because my studio (AKA front room) is of limited size making 200mm lenses impossible to use. The fixed aperture means that there's no increase in depth of field when zooming in, leaving nice sharp images.