A body wave is a seismic wave that travels through the body of the Earth. These are contrasted with surface waves, which travel along across the Earth's crust. Body waves travel out from the focus* of the earthquake, being bent and curved as they pass through varying densities of rock. Once they reach the surface, they give the first indications of the earthquake, although they do not cause as much damage as the following surface waves. There are two main types of body waves:
P waves: the P wave is the primary wave, the first to arrive and the highest in frequency. P waves are compressional waves, as are sound waves; they compress the material they pass through, without moving the material much. The P waves will actually do very little damage, due to their lower amplitudes. These high frequency waves in the ground are probably what dogs and other animals are sensing when they act restless just before the main earthquake hits. Humans can often feel them too, as a shimmy or 'rattle' in the ground.
S waves: the S waves are the secondary waves, and are transverse or shear waves. This means that they cause much more motion perpendicular to the force of the wave than do P waves. They are slower, but have a greater amplitude, resulting in more damage. Even so, most damage done by earthquakes are done by the following surface waves.
Science with Slinky: (Slinky is a registered trademark of Poof-Slinky inc. Go buy a Slinky.) Whether you are browsing Wikipedia or reading a college textbook, the difference between P and S Waves (compressional and transverse waves) will be illustrated through careful scientific manipulation of a Slinky. Don't laugh, it works.
To demonstrate P (compressional) waves, the ends of the Slinky are held between two people, far enough apart that the middle does not droop too much. The two Slinky holders quickly push the ends of the Slinky a few inches inwards towards each other, and then pull them back out. A wave is now traveling through the Slinky, as the coils compress and dilate in a pattern that moves back and forth across the length of the Slinky. Notice that there is very little movement perpendicular to the direction of the wave.
To demonstrate S (transverse) waves, you use the same two people, the same Slinky, but this time the Slinky holders jerk the ends of the slinky from side to side. The slinky waggles like a snake -- lots of chaotic movement to the sides, but you can still follow the wave as it moves along the length of the Slinky. If you find my description confusing, http://www.geo.mtu.edu/UPSeis/making.html has an excellent pictorial diagram.
Applications: These waves can tell us some useful things. First of all, because these two types of waves are emitted at the same time but travel at different speeds, measuring the arrival times of P and S waves can give us a good idea of how far away the focus of the quake is. If you have sufficient measures of multiple P and S waves you can also pinpoint the exact time and location of the focus.
Knowing what kinds of waves these seismic shocks are composed of also tells us about the interior of the Earth, as the waves travel at different speeds depending on what they care traveling through. It is a useful feature of S waves that they cannot travel well through fluid; this led to the discovery, by Richard Dixon Oldham in 1906, that the outer core of the Earth is liquid.
* The focus of the quake is where it starts. The epicenter
of the quake is the point on the surface of the Earth that is most directly above the focus.
Whatever. That is totally not what I was looking for.
Um... A body wave is also a hairstyle, a specific type of perm. While most perms give you very small curls, in a body perm the hair is wrapped around very wide curlers, up to 2-3 inches in diameter. This gives you wavy hair, and is used by those who want to add more body to their hair.