Above are two photos I shot of a dial (of some sort) inside the fuselage of an old Russian cargo plane. Both photos have identical exposure values, but they differ drastically in their image quality. The blurriness of the first photo was not due to missed focus (the focus was fixed for both photos), but rather the natural tendency of my hands to move or shake over time, despite trying to keep still. Because the camera was moving, ever so slightly, the light rays reflected from the subject moved across the surface of the sensor, ever so slightly. This exposed light rays over what would otherwise be a sharp, contrasted edge, blurring the boundary between the dark and light areas. This can be seen when you observe the full resolution crops showing the Russian letters of both photos. With my 35mm lens, the shutter speed was fast enough, at 1/160th of a second, that any natural movement of my hands did not have enough time to register in the exposure for the photo on the right. At 1/5th of a second, my inability to keep my hands perfectly still is obvious in the photo on the left.
In both cases, I was shooting in manual mode, but this is a problem that shows up for those shooting in various automatic modes as well. The automatic modes of most cameras will fire their built in flash if their meters determine an exposure that will need a relatively slow shutter speed (anything below 1/60th, for example), but if your camera doesn't have a built in flash, or you are using a "no flash" automatic mode, then you will may find yourself pressing the shutter release button, and might be surprised when the 2nd "clack" sound of the shutter closing doesn't' take place for a while. If this happens, it is likely you are in a low light environment (such as indoors), and your camera's metering system compensated by opening your aperture to as wide as it can go, and (for digital) your ISO as high as it can go, leaving lowering the shutter speed as the last option for arriving at a correct exposure. When this happens, your only option to prevent blur from camera shake is to find a way to stabilize your camera. Your best option is to mount your camera on a tripod, achieving a stillness no human being could ever hope to achieve. Setting your camera down on a flat, even surface (like a table) can achieve the same result. If a stable platform isn't available, you can steady yourself and your camera by bracing against something solid, like a wall, a tree, or the top of a chair - anything that will introduce another point of contact to keep the various twitching, flexing tendons and muscles fibers throughout your hands and arms from moving the camera.
This next photo shows what you can achieve, even at lower that "safe" shutter speeds (a "safe" shutter speed being anything that is the reciprocal of your focal length, or faster - such as 1/50th or faster for a 50mm lens) if care is taken to stabilize yourself and your camera. This was shot at 1/15th of a second, but you will notice it is much sharper than the 1/5th of a second shot seen in the first photo. Aside from being more careful about holding my camera, it helped that I was using a 35mm lens, which has a wider angle of view and doesn't register camera movement as much as a longer telephoto lens would. If I were using my 70-300mm lens zoomed in to 300mm, then even 1/160th of a second would be too slow for a hand held shot; it would need to be 1/320th or faster. If you've ever looked through a pair of high powered binoculars before, than you'll remember how the slightest movement of your head or hands resulted in the image wildly jumping about. The longer the focal length, the more sensitive to movement your image plane will be.
Aside from tripods and bracing yourself, some digital cameras and lenses have incorporated image stabilization technology, which compensate for camera shake by moving a lens element, or the sensor itself, in motion counter to the motion introduced by your hands. For Canon and Nikon, the image stabilization is built into their lenses; for Pentax DSLRs, the image stabilization is built into the sensor of their camera bodies. This technology results in shots that can be taken at much lower speeds than the reciprocal of your focal length. If my 70-300mm had VR (the Nikon version of image stabilization), I could zoom in to 300mm and shoot hand held as slow as 1/80th of a second. These technologies, as well as the increasingly higher ISO values (allowing for higher shutter speeds) achieved by the latest digital sensors, are helping to make camera shake less of an issue now and in the future.
One important caveat to keep in mind; no matter how stabilized your camera is, only a fast shutter speed can 'freeze' a moving subject. In other words, if your camera is locked down on a tripod, shooting at 1/30th of a second, and the person you're photographing turns his or her head, or waves their arm, it will result in a blurred image for precisely the same reasons camera shake results in blur - light rays moving across the sensor. In the photo below, despite using a shutter speed (1/80th) fast enough for a hand held shot (zoomed to 52mm), it was not fast enough to freeze the motion of the dog or the girl's left foot nearest the soccer ball. The need to freeze action is why sports photographers frequently use massive telephoto lenses - their enormous size due to large glass elements needed to give these lenses a maximum aperture of f/2 or f/2.8, allowing for faster shutter speeds.