Flexitarian: a semi-vegetarian diet focusing on vegetarian food with occasional meat consumption (Wikipedia).
Also, see this Newsweek article.
I realized my first week on the 'Weekday Vegetarian" concept that I could not take it literally. I didn't feel like eating meat when Saturday came around, but on Wednesday I had a scallop spinach salad. Worry about when I was going to have my 'meat-meal' was similar to the damaging concept of having a 'treat meal'. Any meal plan that restricts me makes me batty; I have to have choice. I have to feel better for eating better, not like I 'have' to.
I love the way I feel, and the fact that my skin has totally cleared of any pimples and all eczema since reduced, dramatically, the amount of meat I eat.
Growing up in "I Love Alberta Beef"-land, I was raised on eating meat in at least 2 meals a day- lunch and supper. Let me tell you, since I've eaten meat only 1-2 times a week for the last while, I've not missed out on anything.
If you're looking at trying to reduce your meat intake, try asking yourself why you eat meat- is it a habit? do you enjoy it? And then ask yourself if you'd like to try something new.