That still does not answer the question what makes the heli move in any direction. In the image you can see that when the plane in which the main rotor blades turn is tilted in respect to the ground a resultant force pulls in the direction of the tilt.

The heli will accelerate until the drag, or air resistance, is equal to the resultant force. You have to add power to create that resultant force and a bit more to compensate for the added drag from the main rotor and the tail rotor to keep things in line.

That is what makes flying a basic heli so interesting, you are constanly ´playing´ the controls and power to keep things in balance.