1540s, "plan of action, scheme, design;" 1550s, "ground-plan, drawing, sketch," senses now obsolete, from Middle French plateforme, platte fourme, literally "flat form," from Old French plat "flat, level" (see plateau (n.)) + forme "form" (see form (n.)). These senses later went with plan (n.).
The sense of "raised, level surface or place" in English is attested from 1550s, especially "raised frame or structure with a level surface." Specifically in geography, "flat, level piece of ground," by 1813. The railroad station sense of "raised walk along the track at a station for landing passengers and freight" is from 1832.
The U.S. political meaning, "statement of political principles and of the course to be adopted with regard to certain important questions of policy, issued by the representatives of a political party assembled in convention to nominate candidates for an election," is from 1803. It is probably originally an image of a literal platform on which politicians gather, stand, and make their appeals, and perhaps it was influenced by the earlier sense in England of "set of rules governing church doctrine" (1570s). In 19c., platform was used generally in a figurative sense for "the function of public speaking," and even was a verb, "to address the public as a speaker."