Q:

How do intake deflectors work?

Some turboprop aircraft, for example DHC 6 Twin Otter have “intake deflectors” which should be engaged when taking off from or landing on unpaved surface to prevent foreign object damage. But how does it actually work?

A:

This document describes it nicely. They are also known as inertial seperators:

The nacelle inlet of many aircraft models includes an inertial separator 
  provided by the aircraft manufacturer to prevent heavy particles from 
  entering the engine inlet. Most installations incorporate two moveable 
  vanes, one upstream of the engine inlet and the other blocking the bypass 
  duct. For bypass operation, the inlet vane is lowered and the bypass 
  duct vane is opened permitting maximum separating efficiency. In some 
  installations, the vanes are fixed in the bypass mode. 
As shown in the sketch, air entering the engine inlet must turn sharply past the inlet vane (shown in the lowered position). Particles heavier than air are carried straight through, by their own inertia, into the bypass duct and dumped overboard.
The aft radial inlet design provides many advantages such as superior 
  anti-icing utilizing the principle of inertial separation, low noise levels and unequalled protection from FOD.

