The earth is made of three sections: the outer part or crust, the mantle, and the core. The crust makes up only a very thin section of the earth, sort of like the peel of an apple compared to its flesh and core. The crust is made up of primarily solid rock, as is the mantle. The core makes up the highest percentage of the earth's mass, although the mantle is only slightly smaller. As far as scientists can tell, the outer part of the core is made of molten rock, but the hotter inner core is under so much pressure that it's a solid!
According to the plate tectonics theory, the earth's crust is made of large, continent-sized plates. A fault is a break in the crust caused by plates moving next to each other. Normal faults occur when one side of the fault slides down from the surface. Reverse faults happen when one side is thrust upward. A strike-slip fault happens when plates move sideways against each other. (The San Andreas Fault in California is a strike-slip fault.) See an illustration of all three fault types here.
When two plates hit each other hard enough, they cause an earthquake. The focus of an earthquake is the section in the crust where two plates collide; the epicenter is the point on the surface directly above the focus. Primary waves (p-waves) are the first wave of an earthquake; they travel through the earth's crust, mantle, and core and can be recorded by seismographs on the other side of the world. Next come s-waves, which are slower and only travel through the solid mantle and crust. L-waves travel through the crust and are the strongest waves, with a motion similar to ocean waves. These waves cause the most damage.
You can use a slinky to demonstrate what the movements of p-waves and s-waves look like. With a person holding each end, stretch out the slinky about half way. Now, have one person give his or her end a hard push forward. A compression should form at that end of the slinky and move up the coil, similar to the push-pull movement of a p-wave. S-waves, on the other hand, move back and forth with an undulating motion. Wiggle one end of the slinky. What happens? This side-to-side movement is similar to an s-wave's movement.