Something inexplicable can't be explained. It doesn't make sense. You don't want to come to the beach on the most beautiful day of the year? That's inexplicable!
Inexplicable is made up of the prefix in, which means "not," and explicable, which comes from the Latin explicabilis, meaning "unfolded, unraveled." Do you see the double negative? If something is not unfolded, it's folded up and tangled — like something that doesn't make sense. Your school's decision to call a snow day is inexplicable, if there's barely a layer of snow on the ground.