I tried to find some kind of rationale to the fairy's movements, but I had no luck.
Well you could always look at the source code ;-)
So the game tries to run at 30 FPS.
The fairy has an horizontal speed and is always trying to accelerate. But every click there's a 1/100 chance she changes direction. (the direction it looks like she's facing is determined by her speed not acceleration, i.e. which way she's moving, not which way she's 'trying' to run.)
Every click there's a 1 in 10 chance the fairy tries to jump, but she needs to be on the floor or a box and not blocked, so she doesn't jump all that much.
Her tendency to dive through boxes wasn't planned, just another byproduct of the wonky attempt at a physics engine..
Is there a mute button for the game?