It might be useful to work back from the end result: A print on display. Let's suppose a gallery show... The theory has it that the "best" viewing distance for a print is when the eye's angle of view matches the angle of the lens making the image, adjusted for any cropping. So, you'd stand closer to a wide-angle shot than a telephoto shot. For a print made with a 28mm lens on 35mm film, for instance, you would move in so that the corners form a 75° angle with the eye. For a print made with an 85mm lens on 35mm film, you would stand back so that the corners form a 28° angle with the eye.
This would give the most "natural" viewing perspective, and some print makers size their prints to encourage this, and it may be kept in mind in hanging the show. For instance, a largish wide-angle print hung in a place where the viewer cannot back away, encouraging the "proper" distance.
So why would viewers need to be influenced or forced into the appropriate viewing distance? Because of another factor, now zeroing in on the question at hand...
It turns out that for most people with normal eyesight, the most comfortable viewing for a rectangular flat artwork is from a distance about equal to the object's diagonal. So people tend to position themselves (or hold the item) accordingly.
Using a trigonometric approach, imagine a triangle where the distance from one apex to the opposite side is equal to the length of that opposite side. Bisect the triangle along that distance line. Now to figure the angle at that new apex for which the sine is half the cosine... That's about 26.5°... since the triangle was bisected we need to double that angle to know the original angle of the apex: 53°. Well well, that's the angle of view of a 43mm lens on 24x36mm frame, for which the diagonal is 43mm.
Going at it from the optical approach: The definition of focal length is the distance from the lens's optical center to the film/media/sensor. So if the lens focal length is the same as the media diagonal, that matches the most natural viewing relationship later between eye and print.