Poi is a Hawaiian word for the primary Polynesian food staple made from the stem (called a corm, a type of rhizome) of the kalo plant (known widely as taro). Poi is produced by mashing the cooked corm (baked or steamed) to a highly viscous fluid. Water is added during mashing and again just before eating, to achieve a desired consistency ("one-finger poi" is thicker than "three-finger poi").
Most first-time tasters describe poi as resembling library paste, more an allusion to the texture than the flavor, which tends toward bland. It is an acquired taste, but quickly makes converts of those who persist. The flavor changes distinctly once the poi has been made. Fresh poi is sweet and excellent all by itself. Each day thereafter the poi first loses sweetness and then turns slightly sour. After several days (but no more than five) poi has a distinct sour taste, but is still quite edible with salted fish or lomi salmon on the side. However, some would reasonably argue it is inedible beyond five days. Sourness is prevented by freezing or freeze-drying, although the resulting poi tends to be bland in comparison with the fresh product.
Maori Poi dance, by Manutuke School at Hopuhopu 2003
More information on poi swinging can be found on the Home of Poi website.