I was on a plane recently and took a few pictures from the window. I had the polarizer on initially, and observed this circular rainbow effect:
What is the reason for this?
A sheet of glass or plastics will typically have internal stresses. For glass and some clear plastics these lead to the birefringence patterns you see, when you shine (partially) polarized light on them and then view them through a polarizing filter. You can try this out by either using two polarizing filters, one in front and one behind, or holding such an object in front of an LCD monitor and putting a filter in front. If your filter came in a clear case, that could be a good test object. You can find out more about the topic by searching for "polarizer" and "stress", "stress analysis", or "birefringence". In fact, the Wikipedia article on birefringence has a lot of information and some example pictures.
In your case the sky is providing a partially polarized light source, the airplane window produces the birefringence patterns, and the polarizing filter makes them visible to the camera.