Daruma are round, hollow, traditional paper mache Japanese dolls modeled after Bodhidharma, the founder of Zen Buddhism.
Daruma symbolize patience and strength and never giving up.
Daruma dolls are used in Japan for many purposes, most often for luck at the beginning of an undertaking of some sort.
When the undertaking has been successfully completed, the eyes of the daruma get painted in.
For example, politicians are regularly seen on TV news painting in the eye when they have won an election. Store and restaurant owners place them at the front of the shop.
They are weighted so that even though you push them over they rebound, further symbolizing perseverance.