From my understanding of the term Hue Shifting, it is the nature of coloring an object within a palette that moves about within the space of the color wheel. It allows you to achieve a good mood and establish the cool and the warm lighting of the object while not looking like an overexposed neon shirt from the late-80s. What you're doing with the palette on your character hardly looks like you're doing anything aside from changing the brightness of the blue you're coloring him with. The result, tied together with the low contrast of the colors used, looks like a matte plastic toy cut from a one-color mold in a dimly lit room.
By moving through the color wheel to from one spectrum to another while adjusting the level of saturation and darkness as needed, you can achieve results like these:
Hue shifting allowed me to tweak one palette to move from red and purple shadows to teal and green midtones and highlight with yellow; or one from pink highlights to a royal purple and then shadows hiding in the greenish tones; and then another with a blue highlight, sliding through pink into an orange-brown midtone, and cooling off in a really dark blue.
It's all about jumping around the color wheel by ramping through transitional color combinations.
Check this thread for a little more of an idea how some people/programs handle hue shifts in a more technical sense:
http://www.wayofthepixel.net/pixelation/index.php?topic=10010.msg108254#msg108254
