One of the coolest things demonstrating optical compression is the use of it as a motion picture technique ... where you can see it happen right before your eyes.

I believe it was Alfred Hitchcock that first used it in a major motion picture as a psychological effect in the film "Rebecca" ... when Rebecca suddenly realizes something terrifyingly profound, the lens zooms to a longer focal length while the camera dollies back to keep her the same size ... the visual result is that the background looms up behind her ... a very unsettling sort of effect. Can you imagine the precision required on the part of the camera operators?

Depth of Field can easily be demonstrated even without a lens. Sometimes when I forget my glasses and have to see something small ... I make small circle with my thumb and finger and look closely through it ... effectively "stopping down" my finger aperture to make the object I'm viewing sharper. You can do the same thing with a piece of cardboard and a nail hole. The smaller the hole the more Depth of Field. However, the smaller the hole the more light you need coming through it ... or in the case of photography the longer the shutter has to stay open to record the image.

I knew what was meant, but that does not guarantee that others did. The addition of the words, prospective or visual distance, before the word compression would have made it clear to all. OR the question should have been a simple explanation of the effect after the poster had done a simple google search for "visual compression by telephoto lenses" Google would have responded using the words "prospective distortion." Perspective distortion is a bit more complicated than simple apparent distance between....see:
https://en.wikipedia.org/wiki/Perspective_distortion_(photography)

Looking at your contribution on Toilet Paper, you were brief and complete.... adding a smile regarding unruliness of cats. I am happy that I have been using the correct unroll direction except when I have had unruly cats.
http://www.uglyhedgehog.com/t-442836-1.html

You are most welcome.
I teach photography to novices and teach the joy of the hobby and basic concepts. If they want to get into all the math and esoterics I encourage it but want to develop the enjoyment of photos and basic methods of capturing them again in a fun and enjoyable manner.
I have gone to classes where the instructor gets bogged down in all kinds of math and ratios and things that make the novices eyes roll and they lose interest.
Aperture for example is a pie. Cut the pie in half which is 1/2 is a big piece or opening, f2. Cut a pie in 8 parts 1/8 or f8 and the opening is small so the smaller the f number the bigger the piece of pie or lens opening etc. Obviously there is a bit more but the novice easily grasps the concept and the basis is set.

This will be non-technical and simple.
Look through a wide angle lens and objects closer and further seem to be spaced quite a ways apart. Telephone poles would be a good example. now look exactly the same way and position with a telephoto lens and those poles look to be very close to each other. This is compression. Actually the WA lens is the same if you held the same position. The poles in the far distance if cropped out and enlarged would look the same as the telephoto shot. The WA just shows more. Simply DOF is the range from close to far that all looks focused. Large apertures it is a shallow distance small apertures it is a greater distance of depth. This is different for different lenses but applies to each lens.
There is tons of technical mumbo jumbo and stuff if you want to fry your brain but this is the simple non-technical answer.