One of the advantages of an SLR camera is that when you look through the viewfinder, you see the view that the lens will project on the sensor/film when the shutter is fired. When you do press the button though, the mirror that makes this possible has to swing up and out of the way. The tiny amount of vibration induced by this mechanical function is irrelevant for most work but can become an issue at the high magnification involved with long telephoto lenses and macro photography. If your camera has a mirror lock-up function, it's time to learn how to use it.
If you want to see what mirror slap looks like, firmly mount your camera on a tripod and attach your highest magnification lens, either a big telephoto or a high-power macro lens. Point it at something flat with clear, sharp detail. If you can't find anything convenient, tape a printed page to the wall and use that. You want something flat so that changes of aperture (and thus depth of field) won't contribute to any perceived softness. Now shoot a series of exposures ranging from around 1/250 second up to a couple of seconds. Take shots one stop apart, and use a cable release to rule out any possibility that your finger jiggles anything when pressing the shutter release. Feel free to use a flash if you need more light at the faster shutter speeds. Varying ISO on a digital body if need be shouldn't unduly affect the results so long as you don't go too far overboard.
When you're done, open all of the resulting images and blow them up to full size so you can compare how sharp they are. What you should find is that there is a discernable difference in the sharpness of images in the range of around 1/30 to 1/2 second. Depending on your camera and your tripod, you may not see it unless you look close. The range of affected shutter speeds may be less, but probably not more. Images shot with a fast enough shutter speed will effectively freeze the motion of any mirror vibration. At long enough shutter speeds, the portion of the exposure affected will be increasingly negligible — somewhat like they way a person walking through the frame during a long enough exposure will record as a ghost image or not at all.
The implementation of mirror lock-up differs somewhat between camera models that include this feature, but the basic underlying mechanism is the same. Before you fire the shutter, you use some control on the camera to move the mirror up and out of the way. The mirror movement is the same thing that normally happens at the beginning of the shutter release, but doing it early allows any resulting vibration to dissipate before the shutter starts.
On some bodies, mirror lock-up has to be engaged for each shot you want to use it on, with the camera resetting itself to normal operation after the shutter fires. Other bodies force you to turn on a mirror lock-up mode that will make mirror lock-up active each shot until you disengage this special mode. I have a slight preference to the former strategy, but either will work just fine so long as you know how your camera does things to avoid surprises. Consult your camera manual for details on how yours works.
When the mirror has been locked up, you won't see anything through the viewfinder since the mirror will be blocking it, so make sure you like your composition before engaging mirror lock-up. This shouldn't be a major concern since you won't often be tempted into taking high magnification shots of moving subjects.
Some bodies that lack true mirror lock-up do include an "anti-mirror vibration" setting that moves the mirror up a half-second before the shutter fires. Turning the regular image taking function into a one-two punch that is often sufficient avoid camera movement induced blur. My old Nikon D100 had this feature. If you turn this on without realizing what it does, it may seem that your camera now has an annoyingly long shutter lag, so don't enable this feature unless you mean to. This is a common mistake made by new camera owners so be careful as you explore all the custom settings found on yours. My D2x has true mirror lockup which gives me more control over things, and I'm all about control when it comes to macro work.
Mirror lock-up used to be considered a standard feature for most SLR cameras. But the mirror action of modern cameras is extremely well dampened when compared with cameras made even ten years ago, and camera manufacturers often figure they can save money by omitting the mirror lock-up these days. Canon has it on quite a few models, but Nikon only includes it on their higher-end models. While I wish Nikon would add it to more midrange models, most users of entry-level bodies won't really miss it since they likely won't shoot with lenses that would benefit from it anyway. If you are in the market for a new camera and are planning to get into extreme macro or telephoto work, look for a body that includes mirror lock-up if you can.
Update 06/05/2007 - Reader PS has found an annoying incompatibility between Nikon's mirror lockup and their new Camera Control Pro software:
Re. mirror lock-up: Mirror lock up will definitely reduce blurring in macro photography. However, with the Nikon D2X, the mirror lock up function is incompatible Nikon's Camera Control Pro (computer camera control) software. You can not cause the shutter to close using your computer if the mirror lock up function has been activated. This is annoying when I am photographiing jewelry where I need this program to get instant feedback on how the shots are turning out.