The name is the contracted past participle of the Genoese verb pestâ (Italian: pestare), which means to pound, to crush, in reference to the original method of preparation: according to tradition, the ingredients are "crushed" or ground in a marble mortar through a circular motion of a wooden pestle.
Strictly speaking, pesto is a generic term for anything that is made by pounding; that is why the word is used for several pestos in Italy.