There are three basic ways that companies can be organized: by function, by division, product or geography, or in a matrix. Each has it's particular advantages and disadvantages which I'll point out. We'll look at examples of each.
Your company may not look exactly like one of the examples because of particular business reasons, or for political reasons. Obviously, a manufacturing company will have some departments that a bank or a software company doesn't have and vice versa. Even in very small companies, which tend to be 'flatter' (less hierarchical), you should expect to see roles similar to the examples below. If you are unsure how your company is organized, ask to see the org chart.