They're used when the people making a video want to replace the background with something else. It's very hard to tell a computer where "a person" ends and "the background" begins against normal things, because our clothes might be the same color as background objects. Having one specific color nobody is wearing makes it easier to tell the computer "pick this one color and shades near it and replace those". (You can often see it mess up in Twitch streams if the streamer has a hat or something else that has a shade close to their background.)

Why green? Well, it used to be "blue screen". The difference is analog film vs. digital film. For whatever reason, analog film is better at recording shades of blue and digital film sensors are better at picking up shades of green. Since filming is almost exclusively done with digital equipment now, green screens are more common than blue screens. But it could be any color.

(I think the reason digital sensors pick up green better is they're synthetic. As in, digital sensors are tiny things we build. Our eyes pick up shades of green better than other colors, so we probably decided to design digital image sensors to mimic that. Analog film, on the other hand, is chemicals reacting with light so it's harder or impossible to make them model the human eye.)