Imagine a wave traveling through water. Each water molecule doesn’t really go anywhere. It just gets bumped and jostled by its neighbors and it ends up moving in a circle as the wave passes through.

Light is a wave too. It’s a wave passing through the electromagnetic and mass fields in the same way that a wave passes through water. Light is a vibration that propagates through those fields. So, empty space is an area whose fields aren’t vibrating. The fields are still there just like water is still there when there isn’t a wave passing through it.