What are the functions of the different colored filters in stage lighting?

They serve a lot of different functions, probably the first is to give some depth and texture to the scene. You would ordinarily install lighting for each area of the stage from several directions. Minimally front, side, and back or top lighting. The different directions keep the actors and the set from looking flat, and using different colors from each direction makes it all easier on the eye. The different colors can also help to denote time of day and set an emotional tone. They may also simulate light from sources like lamps on stage or an imaginary source like the sun or an off stage lamp. Another reason is to make one color the predominant light on the actors skin and costumes while using another color to set off the colors on the set. Front light will often use a fairly neutral color, sometimes a warm amber or pink to make skin look nice and for happy scenes, sometimes a color correcting blue to make it a little more like daylight, sometimes a more blue color for night or sad scenes. Top or back light and sometimes side light will often have a deeper color to set the mood or to show off the colors on the set. Then when each scene is put together any combination of these can be mixed together to produce the look the designer and the director want, often in ways that were never planned. The audience usually doesn’t consciously notice a lot of what goes on in lighting, but it is important in setting mood and focusing the audience’s attention nevertheless. Your eyes would get very tired at the end of the show if the lighting never changed, and you would likely have a less emotional experience.

BTW, rent the DVD of Madagascar 2 and either listen to or turn on in subtitles the director’s commentary. They actually talk about lighting the scenes in some places, which threw me a bit because it’s digital, so I never really thought about how they light it. It’s different from stage lighting in some ways, and you can’t see a mix of colors, but if it was a live action film those colors would still be there off stage. There are some scenes where they talk about the emotional tone set by the lights and you can really see the difference in the scene that you would never have noticed had they not mentioned it.

The color filters/gels are used to produce a wide range of colors. Mixing colors of light uses additive color theory. White light is often produces buy using red green and blue lights.