This word, which can be either a noun or an adjective, derives from the French verb tromper, to “cheat” or “delude,” and in English originally meant “fraud” or “deceit.”  From there, by an easily understandable process, “trumpery” took on the sense “worthless stuff, trash, rubbish,” as the OED puts it, and in due course it also came to mean “nonsense,” “intellectual rubbish”; in horticulture, “weeds,” “refuse”; or as a clothing term, “showy but insubstantial apparel, worthless finery” (the OED again).  When in Shakespeare’s The Tempest (4.1.186) Prospero orders Ariel to bring bait for the drunken nitwits Stephano and Trinculo, it’s this last meaning the magician draws on:

The trumpery in my house, go bring it hither
For stale to catch these thieves.

Ariel fetches the clothing, Stephano and Trinculo think it’s mighty fine, but even Caliban (see mohock) recognizes it for what it is: “Let it alone, thou fool!  It is but trash.”

Meanwhile, “trump,” the shorter word within “trumpery” (see sweep), can have the obsolete sense “thing of small value,” but chiefly means a suit of temporary trick-taking power in bridge, or, in another old-fashioned usage, the trumpet, the powerful brass instrument which at the end of time may resound over all creation (“The Last Trump”) but which in ordinary circumstances is sometimes played too loudly, too brazenly.

I am writing this essay in the midst of the primary election campaign of 2016, during which one Republican candidate has come to the fore.  Unless his party’s establishment or the primary voters at large succeed in stopping him, he will be the party’s nominee in the general election:

Perhaps I do not need to explain why at this moment the words “trump” and “trumpery,” in all their meanings—deceit, worthlessness, nonsense, trash, loud brass instrument—come so readily to mind.