To understand what is happening here it is useful to think about the molecules in the air making collisions. The motion of the straw comes from conservation of momentum and the tiny impacts that the air makes with the straw before it escapes.
As you blow down the straw the air exits out the other end. If the straw were straight the air would flow out the end and the straw would stay still. But the air molecules make numerous collisions on the way down the straw - most importantly with the final corner before the air escapes.
As the air molecules hit the bent end of the straw they collide with each other and are sent off in all directions. Some try to head back up the straw and are faced with more collisions, some hit the far end again and some head out towards the exit. Crucially some hit the side of the bend, and this is where the force comes from which moves the straw. As they hit the side, momentum is conserved, they change direction and some of the momentum is transferred to the straw during the impact. As more air molecules hit the side the straw starts to spin. Those molecules that do make this collision rebound off and may escape or may make loads of other collisions before they finally leave the straw.
If you can get the experiment to work by sucking (it is harder to give the air enough velocity - and therefore momentum and force during the collision) the same effect happens. It is the massive number of collisions within the straw at the lower bend which creates the movement. In the case of sucking the molecules are moving up the straw instead of down but the physics and the motion is exactly the same.
Source: NESTA
Date: 16 November 2007
Subject: Physics Engineering
Suitability: Adults/Parents Anyone Over 11s Over 14s Over 16s Over 7s Professionals Teachers