A flexitarian (flexible vegetarian) diet is centered on plant foods with limited or occasional inclusion of dairy and meat. It plays along with other dietary "philosophies", such as ethical omnivorism, as an incrementalist approach to reducing the hazards and negative externalities of feeding oneself.
Meat and dairy are tasty, I know. Trust me, I know. What some may call 'barbecue' is but junk food compared to a traditional south-american churrasco/asado - no steak house will ever replicate it. And cheese? I don't believe humanity will ever produce a passable plant-based canastra cheese. Moqueca, bobó, vatapá... lating american seafood is irreplaceable in my heart.
While meat is indeed tasty, it is a champion of negative externalities in this world - land use, water use, greenhouse gas emissions, animal suffering etc. Seafood and dairy each have their own unique issues too.
Certain aspects of consumption can be offset a little with some investment. Free-range eggs, sustainably produced/harvested seafood, organic/grass-fed cow milk etc are better defaults. But improvements regarding animal cruelty usually also mean a worse environmental impact because factory farming is so efficient.
In terms of health, it is possible to have a healthy diet with plenty of animal products. It's also pretty easy to have an unhealthy plant-based diet. That's why I tend to keep "health" as a concern separate from my vegetarianism. Health is an elusive concept anyway, though there is a health benefit intrinsic to being more intentional with meal planning and paying more attention to our diets.
My average month of meals breaks down approximately into: 20/60 include dairy or eggs, 10/60 have seafood, 5/60 will include meat. Dairy means mostly cheese, as in general our household replaced milk with oat milk except for lattes and desserts. In the eyes of my "carnivore" friends, I'm basically an ovo-lacto-pescatarian that can be tempted into eating meat once a week.
Fully fledged vegans might scoff at such a low bar, but compared to my young adult diet where nearly all of my meals would include some meat and dairy, I'm down on meat consumption by about 90% and overall animal products consumption by two thirds.
Of course, there's more always I could be doing, but while I'm still having an amazing time with my meals, I've already reduced the amount of agricultural land necessary to sustain my lifestyle by about 50%.
That's a lot of impact for such an unambitious change of habit.