Let me start by saying this is by far the hardest drag to understand…
 

Induced Drag- is generated by the airflow around the rotor blade as it creates lift      

The high-pressure (below the airfoil) and low-pressure air (above the airfoil) meet at the trailing edge of the blade                                                                                           

As these 2 air streams rejoin at the trailing edge when they meet this causes vortices. As this air is “shoved down” through the rotor system this averages the relative wind down with the rest of that air stream.                                                       

In other words it pulls or inclines the relative wind downward and rearward near the blade                                                                                                                           

For some reason lift has to be perpendicular (at a 90° angle) to the relative wind.      

This means the lift produced by the blade is perpendicular to the "New Average" relative wind, the lift is inclined aft                                                                                 

The component of lift that is acting in a rearward direction is induced drag                

As the air pressure differential ↑ (↑ AoA more vortices form), induced drag ↑               

Since the blade’s AoA is usually lower at higher airspeeds, and higher at low speeds (except in extremes), induced drag and airspeed have an inverse relationship                                                                                                                       

SIMPLE EXPLANATION IS INDUCED DRAG IS CAUSED BY THE INDUCED FLOW OF THE BLADES AS THEY ARE PRODUCING LIFT (more induced flow, more induced drag).