All gases have mass, and thus take up space.
All gases are elements or molecules that are in a suitably energetic state that they're able to move freely in the space that they occupy. Since these particles have mass, they occupy space.
No matter how many of these particles are present in a cubic metre, they're there, and they occupy whatever space they're allotted. Let us call this space the 'volume', and for the purpose of this explanation, the volume will remain constant. As the concentration, or number of particles increases, then the more of the 'volume' they occupy i.e. the more space they take up.
The movement of these particles within a volume creates pressure, that is, the force the particles exert on the walls of their container as they move around randomly, bumping into one another and the walls of the container. At low concentrations, the pressure will be incredibly low because the particles are not hitting the walls very frequently. At higher concentrations though, the pressure will increase because there are lots of particles colliding with the walls of the container and with one another.
One example that shows how gases occupy space is the process of respiration. Our lungs have a fixed capacity, and although they're elastic and capable of expansion and contraction, there is still a limit to how much air they can hold. Every time we take a breath, gases move to occupy the space that is created by the expansion of the lungs. In order for the gases to diffuse across the alveolar membranes so that oxygen can enter the blood, and carbon dioxide can leave the blood, the gases must exert pressure on the membranes of the blood vessels and alveoli so that they are able to diffuse in and out of the body.
Although in reality it's far more complicated, the short story is that if gases didn't occupy space and exert pressure on their container, then we wouldn't be alive to talk about it.