Xanthan gum is a polysaccharide, meaning it is composed of several sugars linked together. Its structure makes it ideal for thickening, stabilizing, and emulsifying.
When a very small amount is added to a mixture (on the order of 1% by weight), the mixture gains pseudoplasticity--it becomes very viscous, and retains that viscosity when shaken, stirred, heated/cooled. Pseudoplasticity is what gives a bottle of Heinz ketchup its impossible-to-pour quality; without xanthan gum, we would either buy ketchup as thin as water, or as thick as peanut butter.
In the kitchen, xanthan gum can be used to stabilize a foam. By pureeing any fruit or vegetable and blending the liquid you can aerate it enough to create a foam, but without a stabilizer the air bubbles will rapidly deflate.
The appeal of a foam is flavor. Any foam can be added to a dish, imparting its flavor but not physically affecting the dish in any way. Once eaten, the foam "disappears", imparting only its flavor.
To make a foam, combine any amount of fruit juice, vegetable puree, or any other liquid, with .5% by mass xanthan gum. Whip with hand mixer or in blender until desired consistency is achieved.
Example: At WD~50, chef Alex Stupak tops a dessert of braised pineapple and mustard ice cream with a coconut foam.