the time when a person reaches the age at which they have an adult’s legal rights and responsibilitiesCultureThis is usually thought of as a person's 18th birthday. At 18, a person can also vote in elections and get married without the agreement of their parents (though in Scotland people can get married at 16 without such agreement). The 21st birthday might also be thought of as a coming of age, especially in some US states where people are not allowed to buy alcohol until the age of 21. This was also the legal coming of age in Britain until the law was changed in 1969.
See coming of age in the Oxford Advanced American Dictionary