Answer:
Although the question is pretty simple,the answer,I'm afraid, could occupy a whole volume of a book.
But very simply put the secondary sexual growth in males is under the influence of testosterone. Males also produce estrogen but in very small amounts,which makes the effect of estrogen very minimal and almost negligible.
Sexual growth in females is under the influence of estrogen and then progesterone.
In both cases,the physiological process is quite similar:
At puberty in males,the hypothalamus produces gonadotropin releasing hormones which causes the anterior pituitary lobe to produce leutinizing hormones(LH) and follicle stimulating hormones(FSH). LH acts on leydig cells in the seminiferous tubules of the testes to produce testosterone and FSH acts on the Sertoli cells in the seminiferous tubules of the testes to produce androgen binding proteins(ABP). Together testosterone and ABP cause sperm production.
At puberty in females, ,the hypothalamus produces gonadotropin releasing hormones which causes the anterior pituitary lobe to produce leutinizing hormones(LH) and follicle stimulating hormones(FSH). FSH causes growth of the primordial follicle into a mature Graafian follicle while LH presence causes exocytosis of the mature oocyte (ovulation) in about 48hours.