"side of a ship" (technically, "the side of a ship above the water, between the bow and the quarter"), 1590s, from broad (adj.) + side (n.); thus "the artillery on one side of a ship all fired off at once" (1590s, with figurative extensions). Two words until late 18c.
Of things other than ships, 1630s. But oldest-recorded sense in English is "sheet of paper printed only on one side" (1570s). As an adverb by 1870; as an adjective by 1932. As a verb from 1930, "to skid sideways" (intransitive); transitive sense "to strike broadside, collide with the side of" is by 1970.