The simplest way is to take the example of two balloons, one inflated and the other deflated. The inflated balloon needs more space because it has air inside.
Air is a combination of many gases, all of which are matter. The definition of matter is anything that has mass and takes up space. The obvious example is blowing up a balloon. The air occupies the space within the balloon and when enough air is packed into the balloon the membrane of the balloon stretches. This is because no two particles are able occupy the same space at the same time so the particles in the air begin to take up space.