A man continually produces sperm from puberty onwards, with only a gentle decline with age. This is not true of a woman. In a woman, all the egg cells are produced whilst in the womb, and this number progressively decreases thereafter. Bascially, when there are no more egg cells, menopause sets in.
The maximum number of egg cells is reached before birth: around 400 000! This number decreases substantially by the time of menarche (the beginning of periods).
Then, each month during the woman's fertile years, 5-20 oocytes (egg cells) continue their development, principally producing oestrogen. One out of these egg cells will mature fully and be expelled in the hope of meeting up with a sperm cell (ovulation). The others simply degenerate; their function was probably to increase the amount of oestrogen that could be produced.
The next month, the same process starts again - and thus, with every month, many egg cells are lost. Roughly speaking, when all the egg cells are used up, menopause starts. This usually happens somewhere between 45 and 55 years of age, and the symptoms are readily explicable – infertility (since no eggs are expelled) and symptoms of oestrogen deficiency (hot flushes, mood instability, dryness and thinning of the lower urinary and genital tracts, osteoporosis, etc.).
P.S. Why menopause though? It may interest you to know that we are one of only a handful of species that undergo this phenomenon. What is the explanation for this? I have my own bias, and I've written about it here: http://entangledbank.blogspot.com/2007/07/menopause-when-being-mother-isnt-worth.html