What are plate boundaries?

This question almost certainly refers to the boundaries between lithospheric plates, also called tectonic plates. The outermost, solid part of the Earth is called the lithosphere. Large regions of the lithosphere are now known to move relative to one another, sliding on top of the asthenosphere, the layer beneath the lithosphere. The asthenosphere is the upper part of the Earth’s mantle and is described as “plastic,” meaning that even though it is solid, it deforms easily, allowing the plates of the lithosphere to slide on top of it.
Lithospheric plates are large, often millions of square miles. Most of North America is on one plate, for example. Based on the movement of these plates, the continents of the Earth previously all came together and moved apart again.
Lithospheric plates do not move fast—only one or a few centimeters in a year—but they do not all move in the same direction, so interesting things occur at the boundaries, the edges where two plates are in contact. Consider the boundary between two plates that are moving toward one another. This is called a convergent boundary. Something has to happen to the rock from the two sides that is being pushed together. What happens is that either one side subducts—passes beneath the other down into the Earth’s mantle—or else the rock gets pushed together, thickening and moving upward, forming a mountain range. The Alps and the Himalayas were formed this way.
If the two plates are moving apart, molten rock from the mantle wells upward to fill in the gap between them. This is called a divergent boundary. Plates can also move past one another in opposite directions. This is a transform boundary. The San Andreas fault system is an example where the Pacific plate is moving northwest while the adjacent North American plate is moving southeast. This relative motion cases frequent earthquakes as the rocks at the boundary catch on one another and then slip, catching up with the movement of their respective plates.