The ceremony for three-year-old children is called "Kamioki[髪置（かみおき）]" that derives from the ceremony for finishing a custom to shave childrens' hair(There was a custom to shave childrens' hair until three years old in the Edo Period).
"Hakamagi[袴着（はかまぎ）]" is the ceremony for five-year-old boys. Boys wore Hakama[袴（はかま）](Japanese traditional pants, Boys wear Hakama and a Japanese traditional jacket called "Haori[羽織（はおり）]" on Shichi-go-san) for the first time when they were 5 years old and Hakamagi was a ceremony for celebrating that.
And the ceremony for seven-year-old girls is called "Obitoki[帯解（おびとき）]". Girls wore Obi[帯（おび）](sash for kimono) for the first time when they were 7 years old and Obitoki derives from a ceremony for celebrating that.
When Shichi-go-san, children wear formal clothing and most of them wear Kimono[着物（きもの）](Japanese traditional clothing).
It is said that the origine of Shichi-go-san goes back to the Heian Period(794-1185). At that time, the death rate of infants was very high and Shichi-go-san begun as the ceremony for celebrating them who grew up well. And Shichi-go-san came to be widely done in the Edo Period(1603-1868).
It is said that people begun to celebrate Shichi-go-san on November 15 after the ceremony for praying for a child of Tsunayoshi Tokugawa[徳川綱吉（とくがわつなよし）](He was the fifth Shōgun[将軍（しょうぐん）] of the Edo shogunate.), Tokumatsu[徳松（とくまつ）]'s health was held on November 15 (There are various theories.). Now, many people celebrate Shichi-go-san around October and November.
On Shichi-go-san, long red & white candies called "Chitose-ame[千歳飴（ちとせあめ）]" are given to children. The long candies symbolize healthy growth and longevity and red &white are considered auspicious colors. And Chitose-ame are given in a paper bags and auspicious symbols such as cranes & turtles, and pine, bamboo & plum are drawn on that bag.