errand
A short trip to do a specific small task.
To run an errand means to make a short trip to accomplish a specific task, usually something practical like picking up groceries, mailing a package, or dropping off library books. When your mom asks you to run an errand to the corner store for milk, she's sending you on a quick mission with a clear purpose.
People often group several errands together to save time: stopping at the post office, then the bank, then the pharmacy all in one trip. Parents might spend Saturday morning running errands while kids are at soccer practice. The word suggests these trips are somewhat routine or ordinary, not major adventures.
The word comes from an old meaning of traveling to deliver a message, which is why errands have that sense of going somewhere specific to accomplish something particular. You wouldn't call a family vacation an errand, but you would call a trip to return a borrowed tool to your neighbor an errand. An errand has a clear goal, and once you've completed it, you head back.