"If we only played the broomstick, we would only need to use a piston shifting action. However, since we play the violin, we can only use the piston shifting action in the lower positions and in the higher positions the arm needs to move around the violin."
When we shift in the lower positions (between 1st, 2nd, 3rd and 4th positions) the movement is like a piston action (similar to a trombone slide), as it is a simple forward and back movement of the arm along the violin neck. The upper arm comes towards the body when shifting up and the forearm moves directly back towards the scroll when shifting down. This is the basic shifting action in lower positions and it needs to be secure before subsidiary actions, such as independent movements of the thumb, are added.
The only reason that we do not use this 'piston action' for all shifting is that the body of the violin gets in the way in higher positions. To shift to or from higher positions swing the whole arm across the body to the right when shifting up and back to the left when shifting down.