What term describes the musical direction to play very fast?

The term that describes the musical direction to play very fast is "Presto." In the context of tempo markings, "Presto" indicates a speed that is typically between 168 to 177 beats per minute, making it one of the fastest tempo designations in music. This term specifically conveys an energetic and swift execution, often used in lively sections of a composition.

The other terms, while they denote lively tempos, do so at a slower pace. "Allegro" generally means fast, but it is not as fast as "Presto." "Vivace" also indicates a lively tempo but is still a bit slower than "Presto." "Andante," on the other hand, is much slower and translates to a moderate walking pace. Thus, "Presto" stands out as the term that clearly signifies a very fast tempo.