Chemical equilibrium (CE) is the state of a solution (mix of chemicals) such that the composition remains unchanged: a solution that has ongoing chemical reactions is considered in such a state if for each reaction, there is another reaction or a set of other reactions that balances it so that the percentage makeup of each chemical remains the same. Temperature and pressure are generally factors. Given enough time, a solution without other influences (added energy, added material, a source of motion, etc.) is expected to fall into chemical equilibrium, and a characteristic time can often be calculated, i.e., the rate at which it forms.
Chemical equilibrium is of interest in astrophysics in studying the atmospheres (and lakes/oceans) of planets and moons: given enough time, chemical equilibrium is generally expected, and given known reaction rates and expected chemical-equilibrium concentrations, observations of the atmosphere can be validated, or if the expected equilibrium is not present, processes which could keep it out of equilibrium can be inferred. The state of being out of chemical equilibrium may be referred to as non-CE (non chemical equilibrium or NCE). This is reflected in models of such atmospheres: they can assume chemical equilibrium, or may require some presumed instigator of NCE.
The study of the ongoing changes in concentrations in a solution is called chemical kinetics. Stellar models could require some modeling of the chemistry, but much of the stars are sufficiently hot that atoms are dissociated and no compounds are present.
The metal-silicate equilibrium is a factor in the abundances of metals (metals in the "chemistry" sense, e.g., iron) versus silicates in the Earth's mantle: the abundances are considered to result from the equilibrium at the surface between the core and mantle at the end of the core's differentiation.
The term chemical equilibrium is also used in physics and cosmology for the analogous kind of equilibrium, but at a sub-atomic level: particle interactions that create and destroy particles (bosons, atomic nuclei, etc.), i.e., transmute them, e.g., the results of collisions, and spontaneous decaying.
Cosmological models of the early universe posit stages during which the universe was at a much smaller scale and the temperature had to be very high (to reflect the temperatures we see today, that have been diluted by the Hubble expansion), and particles were interacting, eventually losing their equilibrium from the effects of expansion, given established physical laws. Each resulting subsequent chemical equilibrium contributed to abundances of particles and elements and cosmologists aim for models that produce abundances that are still evident today.