Dan Vojtech is a Czech Republic-based photographer who put together a cool visualization to help photography n00bs (myself included) understand how focal length can affect the perceived shape of a subject being photographed.
So Exactly how does focal length impact photographs?
Basically, the smaller the number (ex: 24mm), the “wider angle” the lens will be (capable of capturing a lot of stuff directly in front of the lens. Contrastingly, a larger number (ex: 300mm) will be a “telephoto” lens (capable of zooming in very far, but not able to get a wide view at close distances).
This blog explains it in a lot of detail.
And here is a good explanation from Steven Cooper that details the relationship between focal length and the distance between the subject and the lens.
The reason the subject is occupying the same amount of space on the frame is because each time a longer focal length is used, the photographer is physically moving the camera farther away from the subject. The longer focal lengths actually have a more narrow field of view and so in order for the subject to appear to occupy the same space, the photographer must move back (otherwise you’d get the effect of “zooming in”).
How is that significant? Because the closer you are to the subject, the more substantial the distance between his features are. If you’re only standing 9 inches away from the man, his nose will be very close to you and his shoulders might be 3-4 times farther away from you than his nose; his nose will look quite a bit larger. It’s just like using a forced perspective technique by taking a picture of an arm where the fingers are right up near the lens but the person is standing in front of the lens; his fingers might occupy the same amount of space as his head!
As you physically move backwards, the relative distance of those features to each other doesn’t change but their relative distance to the camera does! Using a 200 mm lens you might need to be standing back a good 20 feet to get a picture like this (just estimating). At that distance, the subject’s shoulders are no longer 3-4 times farther from you than his nose; both his nose and shoulders are about the same distance from you. The result is that the nose gets less distorted and the subject flattens out quite a bit.
…for people who are self-conscious about their weight I tend to use a lens with a shorter focal length and wider field of view because it forces me to get closer to them. Getting closer to the subject causes their body parts to overlap more. Especially for female clients, this generally results in their curves overlapping in more flattering ways. Shooting from far away with a telephoto lens tends to flatten subjects out and make them look heavier.
Source: Dan Vojtech