Primordial nucleosynthesis is one of the key pillars of what's called the Concordance Model of cosmology. It's importance comes from the fact that it predicts specific numerical details of elemental abundance in the modern universe. Only a few elements were synthesized in the early universe: helium plus very small amounts of deuterium, lithium, and beryllium. The fact that such nuclear reactions could take place only when the universe was cool enough for stable nuclei to exist and hot and dense enough for nuclear reactions to take place puts strict limits on the time scale of such reactions: from about 10 seconds after the big bang to about 20 minutes after.
Because the nuclear reactions involved are well understood from laboratory experiments, the observed abundances put tight constraints on the matter density of the universe at that time. In particular, they imply that only about 24 % of the matter density of the universe was in baryonic (proton + neutron) form. It would be a highly improbably coincidence that rotation curves of galaxies and galaxy clusters imply the same proportion of baryons to dark matter. The ratio of neutrons to protons can be calculated at neutrino decoupling (freezeout) from the Boltzman factor exp(- deltaM/kT), where deltaM is the mass difference between neutron and proton and T is the temperature of 1 Mev (roughly 10 billion kelvins), implying about 1 neutron per proton, nearly all of which are scarfed up into Helium 4.
Lots of details here: http://en.wikipedia.org/wiki/Big_Bang_nucleosynthesis