What is the HOMING operator?
The 1993 paper by John R. Koza (a pioneer of genetic programming), Simultaneous Discovery of Detectors and a Way of Using the Detectors via Genetic Programming, can be accessed on CiteSeer. The HOMING operator is described as:


  The one-argument HOMING operator evaluates its argument and, in
  addition, has the side effect of rubber-banding the turtle to its
  position at the start of the evaluation of the HOMING. HOMING is
  equivalent to the brackets in a Lindenmayer system.


From my limited understanding, it is a formal programming operator, within which a certain number of instructions are performed (like motion to North, East, South-West, etc.). It memorizes some initial state (or bookmark), and returns to it when all inner instructions have been executed. In the paper context, it refers to a turtle moving from pixel to pixel to detect a letter in a pixel grid. At the end of its journey, the turtle shall go back to its original location (rubber-banding), or HOME. 

Maybe the illustration of  the bracket effect in an L-system (Lindenmayer system) given in section Turtle branching from Drawing simple generative organics with L-systems can help a bit: