The refractive index of the ionosphere varies rapidly with the frequency of the radio wave (a phenomenon known as dispersion), which means that different frequencies propagate at different speeds. The lightning generates a radio pulse containing many frequencies and as this wave bounces back and forth between the Earth's magnetic poles (like the dashed line in the figure above), the different frequency components travel at different speeds and begin to separate, with the higher frequency waves arriving first followed by the low frequency waves. When detected by a radio receiver and converted to an audio signal, they have a characteristic sound just like a whistle  - hence they are caused whistlers.  

The Radio Astronomy Section has built a whistler receiver that detects the low frequency radio waves and converts them to an audio signal that is output on the internet. You can listen to this radio and maybe you will hear a whistler too. This works best when there is lightning somewhere around Australia.