Looking at 100g chicken breast for example, I see that ~30g is protein and ~4 is fat. What is the rest of the 100g piece made of? Is that all connective tissues? Fiber? Something else?
It's essentially just water.
You can directly see this in the full USDA nutrition facts (link is for "Chicken, broilers or fryers, breast, meat only, cooked, roasted"). Per 100g, there is 65.26g of water, 31.02g protein, 3.57g fat, accounting for 99.85g. The rest is probably just trace nutrients and rounding errors.
You'll see the same kind of thing for other meats. Details vary by cut, but for example here's beef chuck eye steak (64.48g water, 18.86g protein, 16.35g fat), pork loin chops (69.7g water, 20.71g protein, 9.03g fat), and Atlantic salmon (64.89g water, 20.42g protein, 13.42g fat).