The wiki explains it quite clearly. Forward is the direction a model faces and up is the axis along which it stands.
Think of a model facing a top down camera. You get your across which is the X axis and the vertical towards the camera which is the Y axis while the remaining third dimension on the plane the camera is looking at is the Z axis. Models looking in the same forwards direction as the camera will look towards the negative Y values as their forward. Models generally stand with their heads in the positive Z values as their up.
The wiki explains it quite clearly. Forward is the direction a model faces and up is the axis along which it stands.
Think of a model facing a top down camera. You get your across which is the X axis and the vertical towards the camera which is the Y axis while the remaining third dimension on the plane the camera is looking at is the Z axis. Models looking in the same forwards direction as the camera will look towards the negative Y values as their forward. Models generally stand with their heads in the positive Z values as their up.
https://sc2mapster.gamepedia.com/Data/Actors/Site_Operation_(Explicit_Rotation)
As for the exact calculations read the second post of this:
https://www.sc2mapster.com/forums/development/data/233151-values-for-rotation-site-ops
Contribute to the wiki (Wiki button at top of page) Considered easy altering of the unit textures?
https://www.sc2mapster.com/forums/resources/tutorials/179654-data-actor-events-message-texture-select-by-id
https://media.forgecdn.net/attachments/187/40/Screenshot2011-04-17_09_16_21.jpg