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Simply put, if the calories you take in exceed the calories that go out, you'll get fat.
Unfortunately, the actual equation for that is incredibly complex, and the numbers from a calorie counter, some online metabolism calculator, and estimates of exercise is way over-simplified. All you have to do is look at the people you know to see that some people seem to be able to eat whatever they want, not exercise, and still stay skinny. The research backs this up. There are some people who find that on certain diets, a lot of the excess calories are just burned off or passed through. But that's not reliable for everyone.
The main type of food you can reliably eat a lot of and not get fat is non-starchy vegetables:
Alfalfa sprouts
Arugula
Artichoke
Asparagus
Bamboo shoots
Beans (green, Italian, yellow or wax)
Bean sprouts
Beets
Bok choy
Broccoli
Brussels sprouts
Cabbage
Cauliflower
Celery
Chayote
Chicory
Chinese cabbage
Chinese spinach
Cucumber
Eggplant
Fennel
Garlic
Green onions
Greens (beet or collard greens, dandelion, kale, mustard, turnip)
Hearts of palm
Herbs (parsley, cilantro, basil, rosemary, thyme, etc.)
Jicama
Kohlrabi
Leeks
Lettuce (endive, escarole, romaine or iceberg)
Mushrooms
Okra
Onions
Parsley
Peppers (green, red, yellow, orange, jalapeño)
Purslane
Radishes
Rapini
Rhubarb
Rutabaga
Sauerkraut
Scallions
Shallots
Snow peas or pea pods
Spinach
Summer squash
Swiss chard
Tomatillos
Turnips
Water chestnuts
Watercress
Zucchini
SOURCE: https://en.wikipedia.org/wiki/List_of_non-starchy_vegetables
Also, certain fruits are very low calorie and/or high fiber -- it would be hard to eat enough of them to get fat, including:
Lemons
Limes
Tomatoes
Strawberries
Blackberries
Raspberries
Apricots
The other oddity is shirataki noodles, which are almost entirely fiber. They're pretty flavorless, but make a workable occasional substitute for pasta.
What about meat?
Low-carb diets, like Whole30, Atkins, paleo, ketogenic, LCHF (low carb, high fat), carnivore, and others are experiencing growing popularity right now, as many people find that they can eat to the point of being full and still lose or maintain weight (I personally have lost 40 lbs. in 4 months on the ketogenic diet). Steak, bacon, eggs, etc. And eating as much as they want, but... they end up wanting to eat less once they cut out the carbohydrates. Many find that it affects their hunger/satiety and they simply don't want to eat as much, or more importantly, as often. You can have a huge brunch on the weekends if it's the only meal you eat all day. That may be worth trying if you're interested, but it doesn't work for everyone.
If you want something really simple, a way to decide what to eat without having to count calories or macros, or remember a list of allowed foods, try NSNG - No Sugar, No Grains. Yes, you can theoretically still get fat from eating too much fat, but the reality is, if you're not buttering pancakes, frying potatoes, and eating cheesecake, it's really hard to eat enough fat on its own to tip the scale.
Good luck with it!