The light travels from your flash in a straight line, reflecting back at an angle equal to the angle at which it strikes an object. Any highly reflective surface behind your subject, such as glass or mirrors, will reflect the flash back to the camera. This will result in hot spots on your images. If you can't avoid reflective surfaces, angle the flash relative to the surface, causing the glare to reflect away from the camera.
Red eye is an example of this same principle. The flash reflects off of the back of the subjects eye and directly into the lens of the camera. The result is glaring, red eyes. To solve the problem, separate the flash and lens, causing the reflection to return away from the camera. If your flash is not removable, use your camera's red eye reduction feature. If your camera doesn't have red eye reduction, the problem can be minimized somewhat if flash pictures are taken in brightly lit areas, causing the subjects eyes to close down some.
Light falls off, or gets dimmer, as the distance between the light source and subject increases. The flash on your camera behaves the same way, and is referred to as flash fall off. Most flash units are designed to work properly at a maximum distance of 15-20 feet, beyond which the film underexposes. Higher speed films, faster lenses, and more powerful flash units can affect flash fall off, but there is a limit, beyond which your flash becomes useless. For best results, keep flash to subject distances within the 15 foot limit.