When you encourage someone, you give him or her the courage or confidence to do something, like when you encourage your little brother to play harder by yelling his name from the sidelines of the soccer field.
The word encourage comes from the Old French word encoragier, meaning "make strong, hearten." When you encourage the tomato plants in your garden, you water them to promote their growth and health. Encourage can also mean to inspire with hope, like when you encourage your friends to try out for the school play by complimenting their singing and acting talents.