When matter is in a gas phase the atoms are widely spaced out. However, for simplicity it is more convenient to ignore the atomic nature of a substance. Instead it is easier to view matter as continuous and homogeneous substance without any holes. When we do this to a gas we are treating it as a continuum.
The reason why we treat gas as a continuum is because it allows us to assume the properties vary continuously through out the gas. By allowing this assumption there will be no discontinuities that will need to be taken into consideration. However, in order to make this assumption the size of the system must be much larger than the spaces between the gas molecules. Generally this will not be an issue except in special cases.
Example
For example, lets consider a container filled with oxygen. First let’s take a look at the atomic properties of the oxygen atom. An oxygen atom has a diameter that is approximately
Now let’s take a look at the container. At the current pressure and temperature, even if the container was