Providence and provision, and their forebear provide, all ultimately pertain to the notion of foresight. This post discusses these words and others with the same origin.
That ancestor word is videre, the Latin verb meaning “see,” which gave birth to providere (“see ahead”). Provide’s literal sense extended to the figurative meanings of “act with foresight” and “prepare.” The noun form provision, originally used in the context of a church official’s appointment to a position not yet vacant, later also meant simply “something provided” and came to pertain, in plural form, to food supplies provided for a certain purpose, such as an expedition. (One who provides, meanwhile, is a provider.) Proviso, Latin for “provided,” refers to an introduction of a contractual condition or stipulation.
Purvey, cognate with provide, is not as common as the latter word, but one who provides is sometimes referred to as a purveyor, as in a mercantile context. (The word took that form based on a passage through Old French and Anglo-French.) Purview, meaning “a range” or “a limit” or “the essence of a statute,” entered English by way of Old French and Anglo-French, descended from the same word as purvey. Provedore, likely from an Italian dialect by way of Portuguese and Spanish, is a synonym of purveyor, as is proveditore, which in the Republic of Venice also referred to a government official.
Providence, which literally means “foresight,” had an implication of divine guidance as well as a secular connotation first in Latin and then in Old French as well as in English; in the religious context, the English word is often capitalized. Improvidence is the failure to foresee or prepare; the adjectival forms of the antonyms are provident and improvident. Cognate synonyms are prudence/prudent and imprudence/imprudent (the last word not to be confused with the unrelated word impudent, meaning “immodest” or “insolent”), which refer more broadly to discretion, shrewdness, or wisdom or the lack thereof.
Improvisation, and the verb improvise, are also descended from providere, in the sense of improvised, or unprepared, behavior being unforeseen. The truncation improv refers to extemporaneous presentation, especially a spontaneous musical performance or a comedy routine, the latter sometimes based on topical prompts from audience members. (Improve and improvement are unrelated.) By extension, to improvise is to do something without forethought, as when reacting to an emergency or another unexpected situation.