Plyometrics involves increasing muscle power, especially in the legs, by the repeated rapid stretching and contracting of muscles, as by rocket-shipping vertically from a squatting position or explosively jumping over objects. The explosive jumps in plyometrics—which is sometimes called "jump training"—were made popular by the Soviet track-and-field team in the 1970s, who incorporated them in preparing for the Olympic Games. In particular, you might be familiar with the "depth jump," which is used in extreme fitness and strengthening workouts and involves repeated vertical drops from a box or bench followed by an immediate rebound back up. It was created by Soviet coach Yuri Verkhoshansky in the mid-1900s.
The name plyometrics is supposedly a combination of the Greek prefix plio-, meaning "more," and –metrics, which refers to the science of measuring and is influenced by isometrics. By all accounts, the name is a translation of a Russian word by Fred Wilt, a U.S. Olympian who became interested in the Soviet's warm-up and training exercises and introduced them to U.S. athletes and coaches. The etymology of the word isn't very useful in understanding the concept behind the exercise, but its formation may have been influenced by ply, meaning "to exert" or "to exercise," or plicate, which implies folding.