The end-effector of the structure can do 3 translations X Y and Z translations. However more then 1 motor has to be moved in order to execute a pure translation. This means that the desired motions in cartesian space first have to be mapped to the so called joint space only afterwards can these motions be executed as desired. The function that does the mapping is called the inverse kinematic function or inverse kinematic transformation.
This is common in robotics, but not that common for 3 D printers which tend to have a portal type structure. You can read more about the delta robots/delta structure here