Turns Per Second (or TPS) is a measure of the average number of turns per second done during an algorithm or a solve. It is calculated by finding the number of turns (usually in HTM, but also in QTM, STM, or ETM) and then dividing by the time that it took to execute the turns.
Although few people use TPS extensively, it can be an interesting statistic to know exactly how fast someone is turning during an algorithm or even a very fast solve. Once a world record solve has been reconstructed, it is actually possible to look at the TPS and figure out whether the solve was easy (fewer turns than normal) or whether the solver was just turning faster than they usually do.
TPS is also useful to figure out how fast a solver must turn to be a certain speed: for example, if a method takes an average of 50 turns and the solver wishes to be under 20 seconds, they must turn at an average of 2.5 TPS or faster.