A Gimp image may be quite a complicated thing. Instead of thinking of it as something like a sheet of paper with a picture on it, you should think of it as more like a book, whose pages are called "layers". In addition to a stack of layers, a Gimp image may contain a selection mask, a set of channels, and a set of paths. In fact, Gimp provides a mechanism for attaching arbitrary pieces of data to an image, as what are called "parasites".
Images are divided into three basic types, depending on how colors are represented: RGB, grayscale, and indexed. RGB stands for red-green-blue, and indicates that each point in the image is represented by a "red" level, a "green" level, and a "blue" level. Because every humanly distinguishable color can be represented as a combination of red, green, and blue, RGB images are full-color. Each color channel has 256 possible intensity levels (8 bit color depth). There are other programs that allow images to have 16 bit color depth, but Gimp does not currently support this.
In a grayscale image, each point is represented by a brightness value, ranging from 0 (black) to 256 (white), with intermediate values representing different levels of gray.
Indexed images are a bit more complicated to understand. In an indexed image, only a limited set of discrete colors are used, usually 256 or less. These colors form the "colormap" of the image, and each point in the image is assigned a color from the colormap. Indexed images have the advantage that they can be represented inside a computer in a way that consumes relatively little memory, and back in the dark ages (say, ten years ago), they were very commmonly used. As time goes on, they are used less and less, but they are still important enough to be worth supporting in Gimp. (Also, there are a few important kinds of image manipulation that are easier to implement with indexed images than with continuous-color RGB images.)
Gimp makes it easy to convert from one image type to another, using the Mode command in the Image menu. Some types of conversions, of course (RGB to grayscale or indexed, for example) lose information that cannot be regained by converting back in the other direction.
In Gimp, it is possible to have many images open at the same time. If they are large, each image may use many megabytes of memory, but Gimp uses a sophisticated tile-based memory management system that allows it to handle even very large images gracefully. There are, however, limits, and it is usually beneficial when working with images to put as much memory into your system as possible.
A large component of learning how to use Gimp effectively is acquiring the art of making good selections---selections that contain exactly what you need and nothing more. Because selection-handling is so centrally important, Gimp gives you a large number of tools for doing it: an assortment of selection-making tools, a menu of selection operations, and the ability to switch to Quick Mask mode, in which you can treat the selection channel as though it were a color channel, thereby "painting the selection".
All of the commands in the Filters menu, and a substantial number of commands in other menus, are actually implemented by plug-ins.