Actually, there are a lot of things to look for in a "portrait" lens.
1. Focal Length.
Typically, a portrait lens is ideally anything from 75mm to about 150mm. This is the range at which the perspective through the lens replicate how you typically look at people (About 1.5m to 3m away) in actual life. In real life, you don't usually go closer than 1m to someone unless you are intimate with that person; conversely if you are more than 3m away, the person starts to lose his/her visual importance in you field of vision. (All these are just general assumptions, not hard and fast facts).
2. Depth of Field.
In order to make the subject stand out from the background, it's almost critical that a portrait lens have shallow DoF which means wide apertures, from f1.2 to f2.8 usually. The focal length of the lens mentioned early also contribute to this factor. The typical focal range of a portrait lens ensures a good blurred background (bokeh) without turning it into a myriad blur of colour with no distinctive features. Especially so for "environmental"portraits where you will want some relations between the subject and it's surrounding.
3. Lens Design.
A feature of "portrait" lenses is that their iris usually is built with more shutter blades. The "normal"lenses typically have only 6 blades while portrait lens will have more. This iris design is to give a better quality bokeh. If you look at normal lens, you will realise that the bokeh is not as smooth as it should, for small points of colours, you can even see angular shapes. This is because with 6 shutter blades, the aperture formed is not a circle, but a hexagon. It's the same reason why you get hexagonal lense flare. The more blades a lens have, the closer it gets to a circle, and the better graduation between the different colours in the bokeh. Ideally, the lens should have curved blades, but sadly such lense are difficult to made and hence expensive.
There are also other factors such as colour fidelity and brightness, but those are abit harder to observe.
There's nothing wrong with using a 300mm lens to shoot portraits, but imagine how far back you have to stand to even get a half-body shot. Conversely, there's nothing wrong with shooting with a wide angle either, but you have to consider whether your subject is comfortable with you being so close.
