On paper a Graphic Designer is a creative problem solver. We meet with clients, identify their problems (which are normally not what the clients assume they are), and find solutions. For example, a client comes in asking for a new logo because their sales suck. After meeting with the client, you determine that the client doesn't need a new logo at all, their problem is that their packaging isn't appealing to their target audience. You then convince the client that they're wrong, and redesign their packaging to better meet their needs.
When making a design, we commonly work with photographers and copy writers (not to be confused with copyrighters) and our job is to take the raw materials, photographs and copy (meaning: words) and synthesize them into an aesthetically pleasing design. This is where the solid foundation in a lot of different applied arts coms in, because as we all know, sometimes you can't do things right if you don't do them yourself. Graphic Designers commonly get stuck doing the grunt work of writing or rewriting copy and acquiring imagery be it through illustration or photography, especially on smaller jobs because the budget just isn't there.
As you can probably tell, it's a very demanding job, and I'm chained to my computer almost all of my waking hours because of it. I find it rewarding though, it's something I love, eventhough I complain about it a lot. I'm essentially paid to be creative, and I can't think of anything that could suit me more.