The Wheel of Wonder is a certain feature in the game. It is a wheel in the Town Square area of Lamplight Town that gives you a chance to earn free prizes.
To use the Wheel of Wonder, walk up to the wheel. The Wheeler will ask if you want to spin the wheel, and you should click yes. Most of the time, you will earn coins, but sometimes you will be able to win rarer objects.
The Twilight Wheel is very similar to the wheel of wonder, but it contains rarer prizes and can only be spun between certain times.