Number density is a useful concept for thinking about macroscopic samples in a microscopic way. Chemists often try to "visualize" materials with a molecular perspective. Number density can be thought of as the number of particles that are present in a particular volume. As these numbers can be very very large, we typically think of this as the number of moles (a fixed number of particles) within a given volume. This quantity is
$${n\over V}={P\over {RT}}$$
So, if we have any two gas samples that are behaving ideally, they have the same number of particles per volume when the temperature and pressure are the same. For example, if I had two balloons in a room, they would have the same pressure (approximately one atmosphere) and the same temperature (whatever the temperature was in the room). Therefore, they would have the same number density. If the balloons had the same volume then they would have identical numbers of particles. This is really a different way of stating Avogadro's Law.
Consider the following diagram... it consists of 3 identical containers (equal volumes) that each contain identical numbers of gas molecules (also assume the temperature is constant). This is illustrated by showing the same number of circles representing the gas molecules.
Even though the particle sizes are different for each case (think about a real case with helium, neon, and argon), the pressures would all be the same. Why? Because number density is what governs pressure for a gas system where temperature is constant. The number densities here are all the same, 10 particles per unit of volume. However, the particle masses are going to be different and therefore the mass density (see upcoming section) will be different for each gas. Specifically, the larger or more massive the particle, the larger the mass density. So the largest mass density is on the right end and the smallest mass density is on the left end.
It is important to always know whether someone is speaking about number density (mol/L) or mass density (g/mL or g/L). They are definitely related, but they are not the same.