Why do women cease fertility rather abruptly through menopause at an age well before generalized senescence renders child rearing biologically impossible? The two main evolutionary hypotheses are that menopause serves either (i) to protect mothers from rising age-specific maternal mortality risks, thereby protecting their highly dependent younger children from death if the mother dies or (ii) to provide post-reproductive grandmothers who enhance their inclusive fitness by helping to care and provide for their daughters' children. Recent theoretical work indicates that both factors together are necessary if menopause is to provide an evolutionary advantage. However, these ideas need to be tested using detailed data from actual human life histories lived under reasonably 'natural' conditions; for obvious reasons, such data are extremely scarce. We here describe a study based on a remarkably complete dataset from The Gambia. The data provided quantitative estimates for key parameters for the theoretical model, which were then used to assess the actual effects on fitness. Empirically based numerical analysis of this nature is essential if the enigma of menopause is to be explained satisfactorily in evolutionary terms. Our results point to the distinctive (and perhaps unique) role of menopause in human evolution and provide important support for the hypothesized evolutionary significance of grandmothers.