(US) The practice of eating mainly vegetarian food, but making occasional exceptions for social, pragmatic, cultural, or nutritional reasons.
A combination of flexible + vegetarian + -ism. The earliest known use of the term occurred in the October 17, 1992, issue of the Austin American-Statesman, article by Linda Anthony, Acorn serves up 'flexitarian fare'.
English Wiktionary. Available under CC-BY-SA license.