Mission is a term referring to a style of American Arts and Craft furniture. The term may have come from the fact its appearance had similarities to the uncomplicated, solid Spanish missions of California. The term is considered to have been first applied the work of Joseph McHugh but eventually most of the major American Arts and Crafts furniture manufactures used this term in their marketing. The exception is Gustav Stickley who chose Craftsman for the trade name of his line of Arts and Craft furniture. And apparently it is only in reference to Stickley furniture can the Craftsman term be properly used.
I have included three chairs here; the first is a Victorian chair of the 1800’s I found on CSU’s World Images site just to demonstrate how radically different the style was from its predecessors. The second of the lighter wood is a chair that McHugh designed in San Francisco in the mid 1890’s based on the California mission furniture. The third is the version of this chair by McHugh that became so popular that a full line of furniture was designed around it. (The source of the Mc Hugh chairs image is: Rodel, Kevin P., and Jonathan Binzen. Arts and Crafts Furniture: From Classic to Contemporary. Newtown: Taunton, 2003.)
Also, here is link to a PDF on the history of Arts and Crafts Furniture if you want to know more about the history.