Baryonic matter is matter composed mostly of baryons (by mass), which includes atoms of any sort (and thus includes nearly all matter that may be encountered or experienced in everyday life, including our bodies). Non-baryonic matter, as implied by the name, is any sort of matter that is not composed primarily of baryons. This might include such ordinary matter as neutrinos or free electrons; however, it may also include exotic species of non-baryonic dark matter, such as supersymmetric particles, axions, or black holes. The distinction between baryonic and non-baryonic matter is important in cosmology, because Big Bang nucleosynthesis models set tight constraints on the amount of baryonic matter present in the early universe.
The very existence of baryons is also a significant issue in cosmology because it is assumed that the Big Bang produced a state with equal amounts of baryons and antibaryons. The process by which baryons come to outnumber their antiparticles is called baryogenesis (in contrast to a process by which leptons account for the predominance of matter over antimatter, leptogenesis).