Btukfyl

How/why do green screens work? What's so special about the color green that lets us seamlessly replace the background with another image and keep the human intact?

Are there other colors that work similarly?

It's partly about how human colour vision works, partly about avoiding colours you want to keep, such as those of the actors.

Colour cameras record concentrations of red, green and blue light to mimic human colour vision. Before digital techniques, blue screens were preferred because, of the three primary colours, that's the one rarest in human skintones.

When digital cameras were invented, they were given greater sensitivity to green light to mimic a bias in human vision. Green screen doesn't require as much illumination of the screen as blue screen does, which prevents the risk of chroma spill onto the foreground subject's edge, which can cause a special effects failure called a chroma halo.

In the pre-digital era, when the foreground-background distinction had to be much larger than is required today (because of the complicated optical process involved in achieving chroma key), it was almost impossible to get away with any colour beyond blue. Nowadays both colours are very common, with green almost the new default; but, unlike the blue-only era of the past, typically both colours are now on standby.

I may misunderstand the question, but the method of selecting the background based on colour you are asking for is called chroma keying.

In digital post-processing, all pixels which are sufficiently green are considered background and hence treated as transparent. What is "green" is configurable, oftenly in HSV colorspace.

J.G.'s answer elaborates why green usually works best. Blue screens are common, too.

The only video you need to learn more about green screen you ever imagined:

https://www.youtube.com/watch?v=aO3JgPUJ6iQ

This is Captain D. so any attempts to summarize the content are pointless (sorry for breaking the rules).