Z axis is up-down. The Z axis zero point is fully up, at the point where the homing cycle leaves the head. Positive Z coordinates are down. PCB surface level is measured during calibration.
X axis is left-right, Y axis is front-back. X & Y zero point is at front left, where the optical calibration cycle leaves the machine. Positive X coordinates are to the right, positive Y coordinates are to the back, away from operator.
Rotation (A axis) positive direction is counter-clockwise. There is no physical zero point. The A axis zero is where the axis happened to be when the machine was powered on. Therefore, put a mark on the big pulley on the rotation tube and check visually, that it always points to same direction before starting the machine. Although the axis has minimal wobble, this ensures that if there is any, the calibration will work as intended.
Current X & Y position is the down looking camera view center point. The nozzle position is given by the nominal nozzle offset (determined during calibration) plus correction factor (measured separately for each nozzle to correct any runout (wobble)). The exception is the up-looking camera position which is found during calibration. Nominally the up-looking camera position is the machine location where the nozzle, at PCB surface level and without the dynamic correction, is in the middle of view.