Submitted by Frank Cheng, Alhambra, California, and answered by Joann Stock, Associate Professor of Geology and Geophysics, Caltech.
Each plate is moving in a different direction, but the exact direction depends on the "reference frame," or viewpoint, in which you are looking at the motion. The background to this question is the fact that there are 14 major tectonic plates on Earth: the Pacific, North America, South America, Eurasia, India, Australia, Africa, Antarctica, Cocos, Nazca, Juan de Fuca, Caribbean, Philippine, and Arabia.
Each plate is considered to be "rigid," which means that the plate is moving as a single unit on the surface of Earth. We can describe the relative motion between any pair of plates. For example, the North America plate and the Eurasia plate are moving away from each other in the North Atlantic Ocean, resulting in seafloor spreading along the mid-Atlantic ridge, which is the boundary between these two plates. In this case, if you imagine Eurasia to be fixed, the North America plate would be moving west.
But it is equally valid to imagine that the North America plate is fixed, in which case the Eurasia plate would be moving east. If you think about the Pacific–North America plate boundary (along the San Andreas fault in Southern California), the motion of the North America plate is different; the North America plate is moving southeast relative to the Pacific plate.
This doesn't mean that the North America plate is moving in different directions at once. The difference is due to the change of reference frame, from the Eurasia plate to the Pacific plate.
Sometimes we describe plate motions in terms of other reference frames that are independent of the individual plates, such as some external (celestial) reference frame or more slowly moving regions of Earth's interior. In this case, each plate has a unique motion, which may change slowly over millions of years.
Technically, the plate motion in any reference frame is described by an angular velocity vector. This corresponds to the slow rotation of the plate about an axis that goes from Earth's center along an imaginary line to the "pole" of rotation somewhere on Earth's surface.
