Role of FSH and LH

FSH/LH's role in females;

FSH (Follicle Stimulating Hormone) stimulates the follicle to secrete the hormone oestrogen. It also helps toward regulating the menstrual cycle.
LH also plays an important role in the menstrual cycle. 
During this cycle, LH (Luteinizing Hormone) levels rise. This causes the egg in the ovary to complete Meiosis I. About two weeks later, LH levels surge; this sudden rise in LH triggers ovulation.
LH also turns the follicle into a corpus luteum; this corpus luteum will then release progesterone.

FSH/LH's role in males;

FSH, along with testosterone, is needed for spermatogenesis (production of sperm). It stimulates the process to occur.
LH triggers the Leydig cells of the testes to produce and secrete testosterone, which is essentially needed for sperm production.