Let's take a look at verses that discuss coming of age for children.
For boys, it is Genesis 17:25
YLT Gn 17:25 and Ishmael his son is a son of thirteen years in the flesh of his foreskin being circumcised;
And for girls it is obviously defined by start of their period, which also occurs normally around 13 years of age.
At this age, boys and girls become men and women and become responsible for their own actions. They are now responsible to keep all Written Torah commandments.
The reason why children less than 13 years of age are not responsible is stated in Deuteronomy 1:39.
YLT Dt 1:39 'And your infants, of whom ye have said, For a prey they are, and your sons who have not known to-day good and evil, they go in thither, and to them I give it, and they possess it;
For boys, there are few other levels of maturity according to the Torah. First is when they become eligible for military conscription at 20 years of age. Its Numbers 1:2-3
YLT Num 1:2 'Take ye up the sum of all the company of the sons of Israel by their families, by the house of their fathers, in the number of names--every male by their polls;
YLT Num 1:3 from a son of twenty years and upward, every one going out to the host in Israel, ye do number them by their hosts, thou and Aaron;
Second, when descendants of Aaron are eligible for Service of the Sanctuary (service in the Tabernacle) at 25 years of age. It is Numbers 8:24-26
YLT Num 8:24 'This is that which is the Levites': from a son of five and twenty years and upward he doth go in to serve the host in the service of the tent of meeting,
YLT Num 8:25 and from a son of fifty years he doth return from the host of the service, and doth not serve any more,
YLT Num 8:26 and he hath ministered with his brethren in the tent of meeting, to keep the charge, and doth not do service; thus thou dost to the Levites concerning their charge.'So, as you can see, the division is as follows:
- 13 years old(first period for girls). This is the age when children become adults, have to observe all Torah commandments and can have sexual relations (age of consent).
- 20 years of age. This is the age when men are ready for military service and eligible to kill.
- 25 years of age. Mature enough to serve in the Tabernacle.