send (one) on an errand
To instruct or direct one to go out on a short trip in order to perform some specific task. The boss sent me on an errand to have these documents notarized. A: "Where's Tom?" B: "Oh, I sent him on a few errands around town. He should be back in a couple hours."
send someone (out) on an errand
to dispatch someone to perform an errand. Jerry will be back in a minute. I sent him out on an errand. Who sent you on an errand?