A circumstance is the condition in which something happens. Say you were at a business luncheon and you were accidentally fed psychedelic mushrooms in your ravioli, your boss might excuse the weird things you said, given the circumstance.
Circumstance comes from the Latin meaning the conditions around something. If you are born in a war zone, you're born into a difficult circumstance. If you're making decisions about awarding a scholarship to the most needy person, you'll need information about each candidate's circumstances. If you didn't do your homework because the power was out all night, tell your teacher that under the circumstance, you couldn't see well enough to read.