a short and quick trip to accomplish a specific purpose, as to buy something, deliver a package, or convey a message, often for someone else.

the purpose of such a trip

He finished his errands.

a special mission or function entrusted to a messenger; commission.

noun

assignment , charge , commission , duty , job , message , [[missionnotes:an errand is a short trip that is taken for a specific purpose; arrant means thoroughgoing - downright - out-and-out - extreme - notorious; errant means wandering or roving especially in search of adventure - deviating or straying from an appointed course - straying from the proper standards - moving aimlessly or irregularly]] , chore , mission , task