What must a mechanical wave travel through

A mechanical wave always consists of wiggles in some kind of material stuff. The material stuff may be air, water, rock, wood, steel ... almost anything, as long as it's some material. In general, whatever the waves are moving through is called the "medium". If there isn't any, like the vacuum in space, then mechanical waves can't travel there. For example, sound can't travel in space ... not even an inch.