Secondary atmosphere
A secondary atmosphere is a planetary atmosphere that did not form directly via accretion during the formation of the planetary system. It is characteristic of terrestrial planets such as the four planets of the Inner Solar System, i.e. Mercury, Venus, Earth (specifically Archean Earth) and Mars, as these planets typically are not massive enough for gravity to long-lastingly retain the compositions of their initial primary atmospheres.
When a protoplanet forms from coalescence of planetesimals, it begins to achieve sufficient mass to also accrete volatile gases from the protoplanetary disk, which envelope the planetary surface forming an atmosphere with primordial ("protosolar") compositions identical/similar to the original circumstellar disk, i.e. the primary atmosphere. Due to ongoing atmospheric escape, outgassing from internal volcanic activities, chemical reactions among the volatiles, and/or meteoric introduction of foreign volatiles from impact events with comets and asteroids, the primary atmosphere will experience gradual alterations to its compositions over time, and a secondary atmosphere forms when the accumulated alterations are significant enough.
The secondary atmospheres of terrestrial planets are relatively thin compared to their original primary atmosphere, and are significantly thinner than the contemporary atmospheres of gas giants like Jupiter and Saturn, which tend to retain their primary atmospheres. The atmospheres of ice giants such as Uranus and Neptune are similar to those of gas giants in hydrogen and helium proportions, but tend to be proportionally thinner than the gas giants and have much higher levels of atmospheric methane.
The current atmosphere of Earth, which is uniquely oxygen-rich (with a molar fraction of 20.9%), is actually not its secondary atmosphere, but rather a tertiary atmosphere that formed by further alterations to the secondary atmosphere, most notably by the appearance and evolution of biological life. The Earth's secondary atmosphere started to form during the Hadean eon after the Theia Impact, which caused partial ejection of the original primary atmosphere and was followed by significant outgassing through the post-impact molten mantle throughout the Hadean, and eventually significant foreign volatiles injection via a "late veneer" of extraterrestrial impactors at the end of the Hadean. With subsequent crustal cooling and solidification, the Early Earth's atmospheric temperature and pressure dropped to condense out most of the water vapor (which precipitated onto the surface forming a superocean), leaving a nitrogen/methane/CO2-dominated reducing atmosphere during much of the Archean eon, i.e. the Earth's secondary atmosphere. However, when cyanobacteria evolved during the Mesoarchean, their chlorophyll-driven photosynthetic carbon fixation continuously released elemental dioxygen as a byproduct of water-splitting, eventually overwhelmed the Earth's surface reductant capabilities and led to the Great Oxygenation Event at the end of the Archean. With further radiation of photoautotrophs (cyanobacteria and their symbiogenetic relatives, i.e. algae and plants), the Archean secondary atmosphere (prebiotic atmosphere) had been transformed into the oxic tertiary atmosphere (which is an oxidizing atmosphere with significant biotic inputs within its circulation) during the Proterozoic and Phanerozoic eons.