A wet coating must spread over a surface and then become a useful film. Three roles help explain it: pigments provide colour and hiding, the binder holds the film together, and a liquid carrier makes application possible. Paint also contains additives and may contain extenders, so this is a model of its main roles, not a complete recipe.
In a typical water-based emulsion, polymer particles are dispersed in water. As water leaves under suitable conditions, those particles come together to form a film. Traditional alkyd paint also hardens through reactions involving oxygen. Formulations overlap; “water-based” does not describe every detail of curing.