Lean manufacturing - basically reduce waste in the manufacturing process, either with materials or to reduce the number of processes.
http://en.wikipedia.org/wiki/Lean_manufacturing
Update offsets is probably referring to tooling offsets. As the tool wears, it's tolerances and shapes change. There are also other offsets stored in CNC machines.
Not sure about pick up zeros.
FANUC is a large robotics company. The HAAS CNC machines (milling centers / drilling centers / toolroom lathes) that I used for my CAM courses at RPI used FANUC controllers.
Hope this helps.
