"maker of pots, one whose occupation is the making of earthenware vessels" (they also sometimes doubled as bell-founders), late Old English pottere "potter," reinforced by Old French potier (Anglo-French poter) "potter," both from the root of pot (n.1). As a surname from late 12c. An older Old English word for "potter" was crocwyrhta "crock-wright."
Potter's field "piece of ground reserved as a burying place for friendless paupers, unknown persons, and criminals" (1520s; early 14c. as potter's place) is Biblical (Matthew xxvii.7), a ground where clay suitable for pottery was dug, later purchased by high priests of Jerusalem as a burying ground for strangers, criminals, and the poor. [Purchased with the coins paid to Judas for betraying Jesus; these being considered blood money it was then known in Aramaic as Akeldema, "field of blood."]
The ancient Athenian city cemetery also was a "potterville" (Kerameikos), and there seems to have been an ancient association of potters' workshops with burial places (Argos, Rhodes, etc.; see John H. Oakley (ed.), "Athenian Potters and Painters," vol. III, 2014). Perhaps both were kept away from the inhabited districts for public safety reasons (disease on the one hand and on the other fires sparked by the kilns).
"occupy oneself in a trifling way, be busy in doing little," 1740, earlier "to poke again and again" (1520s), apparently frequentative of obsolete verb poten "to push, shove, poke," from Old English potian "to push" (see put (v.)). Related: Pottered; pottering.