The old mantra that "the camera adds 10 pounds" isn't entirely off base, depending on how you're shot. As photographer Dan Vojtěch highlights, your focal length and distance from your subject can dramatically affect how they look. Photo by Brad Montgomery.
The reason for this has to do with the way cameras compress space in a certain focal length. If you use a short focal length like 20mm, you have to be very close in order to focus properly. From this distance, the tip of a person's nose may be several times farther away than the backs of their shoulders.
If you've ever seen The Lord of the Rings, you might be familiar with how this distance can affect how body parts are perceived. Simply put, the farther away from the camera an object is, the smaller it looks. This is the same trick they used to make full-size Elijah Wood seem Hobbit-sized while standing next to Ian McKellen. By the same token, if your subject's nose is the same distance from the camera as their shoulders are from their nose, their shoulders might start to look smaller. This can compress the face and body to look smaller than it is (and, consequently, probably make the nose look bigger).
On the other hand, if you use a longer focal distance, you'll need to be farther away from the camera in order to make a proper shot. This can make body parts start to overlap and seem more compressed, but it can also accentuate certain body parts. If you're shooting a metre or so away from your subject, the centimetres between their nose and their shoulders won't seem as far apart, so their proportionate size will appear different to the camera.
There's no "correct" focal length or distance to shoot from, so you can't just pick one for the most flattering shot, but it's something you can toy with while you take pictures. Check out Dan's post below for a selection of photos that highlight the difference that focal length can play on your portraits.