1550s, "engagement to marry," a variant of ensurance "an assurance, pledge, guarantee," from Old French enseurance "assurance," from ensurer, from en- "make" (see en- (1)) + sur "safe, secure, undoubted" (see sure (adj.)).
Commercial sense of "security against loss or death in exchange for payment" is from 1650s. Assurance was the older word for this specific sense (late 16c.). Compare insure.