The term nucleosynthesis refers to the formation of heavier elements than hydrogen.
One second after the Big Bang, the temperature of the universe was roughly 10 billion degrees and was filled with a soup of neutrons, protons, electrons, anti-electrons (positrons), photons, neutrinos and other particles. As the universe cooled, the neutrons either decayed into protons and electrons or combined with protons to make deuterium (an isotope of hydrogen). During the first three minutes of the universe, most of the deuterium combined to make helium with trace amounts of lithium.
The predicted abundance of deuterium, helium and lithium depends on the density of ordinary matter in the early universe. Studies indicate the abundance of helium is relatively insensitive to the abundance of ordinary matter, above a certain threshold. We generically expect about 24% by mass of the ordinary matter in the universe to be helium produced in the Big Bang, consistent with observations.
Given a precise measurement of the abundance of ordinary matter, the predicted abundances of the other light elements becomes highly constrained. The WMAP satellite is able to directly measure the ordinary matter density and finds a value of 4.6% (±0.2%), indicated by the vertical red line in the graph. This leads to predicted abundances shown by the circles in the graph, which are in good agreement with observed abundances. This is an important and detailed test of nucleosynthesis and is further evidence in support of the Big Bang theory.
Why Nucleosynthesis in the Early Universe Cannot Account for Abundances of Heavier Elements
Elements heavier than lithium are all synthesized in stars. During the late stages of stellar evolution, massive stars burn helium to carbon, oxygen, silicon, sulfur, and iron. Elements heavier than iron are produced in two ways: in the outer envelopes of super-giant stars and in the explosion of a supernovae. Most elements could not have been made in the early universe. Neutrons decay in about 10 minutes, and their density decreases as the universe expands in that time. There just isn't enough time to keep building up to the heavier elements before the neutrons are gone. The heavy elements are made later, in stars.