What is meant by bandwidth here?
If you filter the signal over a certain bandwidth the noise power is proportional to the bandwidth. They are assuming white noise (constant power spectral density). So the noise power between 0Hz and 1MHz is the same as the noise power between 1MHz and 2MHz and half that between 1MHz and 3MHz. 

In a sampled data your analog anti-aliasing filter may be designed to block signals that approach fs/2 or less, or you might be undersampling. If you are undersampling you likely have an anti-aliasing filter that is a bandpass filter, to the same effect, the noise power is proportional to the bandwidth of the analog filter. 

Real noise power usually includes a 1/f component, may not be all that constant with frequency, and always declines at high frequencies (or the power would be infinite).