The flexitarian diet is a plan that limits meat and fish, but does not completely eliminate it. The major focus is to add more plant-based foods, and since it allows for occasional meat and fish, it may be easier for people to follow and stick to the plan.
There are different ways to incorporate this into your lifestyle–some people have specific days of the week that are non-meat, like “meatless Monday”–others follow a regimen of every other day including a animal protein. I also knew of a person who followed a vegetarian diet for one week and then allowed animal protein into her meals the following week.
For more details, check out the book, entitled “The Flexitarian Diet”, written by Dawn Jackson Blatner, who developed this diet.