Is designing/drawing characters and backgrounds for video games a part of graphic design?
I want to work as a designer of videogame characters and backgrounds, but I don't know if there is such a job, or what it is called (illustration, graphic design, concept design?).
I am about to go to college, but I don't know what I need to learn or study to do this job. Is there a specific major or subject that is going to help me in this?
Short answer: Yes, there is such a job (2D Concept Artist/ Illustrator, although the title varies), and the only thing you need to get into it is probably a good portfolio of illustrations. A degree in Arts or Design helps too.
Long answer: Ask yourself why exactly you want to be a video game designer. What is it about it, compared to other areas, that you particularly enjoy?
Graphic Design is a very broad field. From the group of people that work as designers, some have a degree in design, others have a degree in something else (like development, or any other area) and a few just don't have one at all.
Game development/design is a small(ish) field, although apps make it easier for almost anyone to create a game and put it up in a store. But until you can work as a game designer (and nothing else but a game designer) you will have to work as a lot of other related things. And I think this is why you need to figure out what you like about this particular field.
Do you like drawing? Do you enjoy learning about illustration? If so, then the best thing you can do to get started is... practice practice practice. Get a tablet (a small one should do) and start creating things, get together a portfolio to showcase your work. An art degree would be better in this case (but think of what you would like, what would motivate you).
Do you like design? Do you find typography, web, print and so, interesting? If so, you might really enjoy a degree in Graphic Design. In both cases, the best part will not only be the techniques you will learn, but the people with similar interests you will meet.
It's important to know what the industry wants, but it's more important to know what you want. I think Uni is great, it just changes your vision of the world, if you can study, DO IT. But keep in mind that a degree doesn't necessarily get you a job. Ideas, projects and initiative open more doors. Find a developer friend, or a group of people with ideas and energy, and create a game together. You don't need to wait until you have graduated, the best thing you can do (IMO) is start right now. That way, when you have graduated, you can say: This is what I like, and this is what I've done.