This is a right-handed 3D coordinate system fixed in the telescope such that when the telescope is at the horizon, Y is pointing into the ground, Z always points along the telescope optical axis towards the sky, and X completes the right-handed triple. The origin of this coordinate system is the intersection of the (vertical) azimuth axis of rotation and the (horizontal, rotating) elevation axis of rotation. This point should lie on the surface of the tertiary mirror.
This is the coordinate system in which telescope surveys are carried out. It is also the coordinate system in which ACS mirror positions are defined. Its X and Y are related to the (Az,El) coordinate system in that, ignoring small telescope misalignment errors, the telescope X axis points in the positive azimuth direction and the telescope Y axis points in the negative elevation direction.
See Telescope coordinate systems looking towards sky (excludes Nasmyth foci) ignores these small errors and marks one axis as Az and -X and another axis as El and Y (the signs have changed from the previous paragraph; read on!). What this means is that
In the focal plane it is not possible to ascribe meaning to the (X,Y) coordinate system, and on the other side of focus the (X,Y) directions change sign.