Liquids provide a visually appealing way of moving the glowsticks in mid-air.
Liquids in the non-glowstick, dancing form means giving the illusion that two hands are following a path that looks very watery. The figure 8 is simply a liquid that follows a path. The inverted-figure 8 is in my opinion, a liquid version of the figure 8 that looks pleasing to the eye.
In terms of glowsticking, liquids are accomplished usually by having two glowsticks follow each other. This can be done in a multitude of different ways.