Of or pertaining to James Smithson (c.1765–1829), British mineralogist and chemist whose bequest was used to set up the Smithsonian Institution in the United States.
"The historic documents reveal that many early artifacts were cataloged by a smithsonian before the institution was officially established."
In plain English: Smithsonian describes anything related to the huge group of museums and research centers run by the United States government.
"The Smithsonian Institution features many famous Smithsonia exhibits about American history and science."
The Smithsonian Institution, a group of museums and research centers established in 1846 and administered by the United States government.
"Visitors flock to the Smithsonian every day to explore its vast collection of museums and research centers."
The word smithsonian combines James Smithson's name with the suffix -ian to form an adjective meaning "of or relating to him." It entered English specifically to describe institutions and collections associated with his bequest.