I heard that some foods burn calories? But is that true, and what foods are these?

There are no negative foods. All food has calories, though some, like celery, have so few calories it hardly seems worth the effort of eating them.

Interesting, one study found that when people estimated the calories in a meal accompanied by a salad or celery or a piece of fruit, they thought the meal had fewer calories than the same thing without the salad etc.

Green vegetables have a huge number of health benefits and are very filling for the number of calories in them, so these are foods to fill up on.

So do some of these foods burn more calories by digesting them than by consuming them?

No, nothing that is an actual food burns more calories to digest than they provide. Things like celery, rhubarb, spinach, cabbage, fennel, mushrooms etc have extremely low amounts of calories for the amount of food they provide, so they are useful if you are cutting calories.

The closest thing to a negative food is ice cold water. It doesn't provide any calories, but your body has to expend some in order to heat it to body temperature.