Here is an oversimplified and unscientific definition of FSH:
FSH stands for follicle-stimulating hormone. It is a hormone that is produced by the pituitary gland that, in the female, stimulates the ovaries to develop a follicle (the housing that accompanies the egg prior to ovulation) – each month. It can be thought of metaphorically as the gas pedal which causes the ovaries to ovulate each month. As women age, it becomes more difficult for the ovaries to ovulate as the supply of eggs gets reduced and so the level of FSH rises (in order to push down the gas pedal further) over time. When a woman enters menopause, her ovaries are depleted and the gas pedal stays depressed permanently; that is to say the FSH level remains high. It is also possible for young women to have prematurely high FSH.
A more technical definition can be found in this article on Wikipedia.