You have asked a pretty deep question in a way. I have spent a bit of time trying to write out the issue for you. I hope it helps. Sorry up front this is so long but I do not see this as a simple answer question if we are all interested in learning how and when to use filters. Stick with me here!!!!!
I am going to preface this with a statement, all filters, lenses, flashes, camera bodies, you name it are tools that can be used to accomplish a goal or look. But, a quick history lesson if I may. In film, you were locked to specific issues. You would choose your film based upon the type of shooting you would do. It was film. It was what it was and you had to pick different film for different purposes. Some films shot warm colors (more orange in it) other film shot colder (more blue in it). Some films that shot blue were designed to shoot indoors under incandescent lighting and it would correct for all the yellow from the lights. That all said, many filters were developed for MANY corrections and looks. During those times it was always a test to see what the picture looked like “straight out of camera” SOOC for short. It showed the ability of the photographer to read the existing light and conditions and make corrections based upon the film they were using.
That said, when digital photography came onto the scene, the array of tools exploded. Film is no longer the market share of photography, but instead it has been replaced by sensors. Since a sensor is nothing more than a light receptor attached to a mini computer inside your camera, suddenly programs, color corrections, and modes became available since we were dealing with a digital image and not burning physical film with an exposure. Since the image is computer generated inside the camera, it can also be computer manipulated on a computer later. All color cast filters of old can now be recreated very nicely in any basic photo processing program. The orange acts as a warming filter if it is not to strong. It also helps with blue color cast such as if you are under tungsten lighting. The blue filter helps in areas under incandescent lighting. It can help remove some of the yellow color cast they tend to throw. Depending on the flash you are using, a yellow or orange filter could also help remove some blue cast that is often thrown by a flash unit. Do be careful, you may find that depending on your camera’s abilities, your camera will read the shot, automatically set your camera to a flash setting and add some yellow or orange to balance the color. Put an orange filter on the front and your pictures look orange since the camera already added color due to the flash setting. SO, with digital does that make color filters obsolete?? Not in my opinion. It means you now have at least two tools to use to correct color rather than one in the “old days”. Most find it easier to color correct in the camera or in the computer but again, it is not a wrong thing to learn to read a scene and color correct with filters. Even all of the soft focus, center spot focus, star, prism, and the other multitudes of special affect filters can be recreated in a photo program. It also depends on how much time you want to spend at a computer finishing your pictures.