Literally, "apod" means "without legs". In this particular context, it is the study of how creatures without legs move -- typically, it is the study of how snakes
Snakes typically have 80 to 120 vertebra that individually can not turn more than a few degrees. Furthermore, they can mostly only turn in the horizontal plane -- parallel to the ground. Yet somehow these snakes can manage, through actuating their muscles in the correct sequence to move forward at high speed, while simultaneously avoiding obstacles such as rocks. Snakes can also "sidewind" -- moving sideways relative to their heads. It also turns out that apod motion is very energy efficient: Since the snake does not have to lift its own weight every time it moves, it doesn't take much energy to move along.
It is hoped that the study of apod motion will lead to new robot designs. Apod robots would be very useful for certain types of search and rescue operations, especially ones with narrow spaces.