Maturation is the process of growing up and becoming fully developed — not the finished state, but the stretch of time during which the growing happens. It is a formal, technical word. Where you would say in ordinary English 'children grow up at different speeds', a textbook says 'the rate of maturation varies'. That is the real difference between this word and 'growing up': the register, not the meaning. You meet it mostly in three places. In biology and medicine: the maturation of cells, of the brain, of an insect. In psychology and education: emotional maturation, the maturation of language skills. And in food and drink, where it means the slow improvement that comes with time — the maturation of cheese, wine, or whisky in barrels. Note it is normally uncountable ('a period of maturation'), and you talk about the maturation OF something. English also has a plainer noun, 'maturity', and students mix the two: maturity is the state you arrive at, maturation is the journey there. A twenty-year-old has reached maturity; the brain's maturation continues into the mid-twenties.