The cartwheel effect is a term that describes the rotating, windmill like effect of light that mint state coins exhibit. The cartwheel effect is best known for appearing on Morgan Dollars, due to a fortuitous confluence of coin design, planchet size, and die preparation methods, although the effect can be seen on nearly any mint state coin. The cartwheel effect is caused by flow lines that occur during the coin striking process, and the effect is somewhat fragile, disappearing as a result of circulation or the coin being cleaned.
To most easily observe the cartwheel effect, hold a newly minted coin with the obverse side up, and tilt the coin at various angles to the light. You should see a pattern of rotating lighter versus darker reflection of the light against the coin's surface as you tilt the coin. The cartwheel effect is best seen on larger coins, and doesn't necessarily appear on all mint state coins, since the effect is dependent on various factors that come together during striking.
See also: The Cartwheel Effect & How to Tell if a Coin Has Been Cleaned.