There is a wikipedia on flexitarians. They have changed it to semi-vegetarianism. The wiki on flexitarians used to have have more information/history about the word “flexitarian.” I think it is important (did I mention I was from Austin) so here is a brief history that is often left out of the discussion.
There was a small restaurant in Austin, Texas called the Acorn Cafe (26th & Guadeloupe). A reporter from the Austin American Statesman was doing an interview/review of the restaurant. The owner Helga Morath referred to her food as “flexitarian fare.” The reporter Linda Anthony quoted Morath in her article. This was in 1992 (Oct 17) and the word has continued to been used down in Austin since that time. Over time it has become more and more popular. In 2003 the word was voted the most useful word for the year by the American Dialect Society defined as a vegetarian who occasionally eats meat.
More commonly (especially in Austin) I heard it to describe someone who tried to eat less meat for various reasons that were usually health and financial related.