Lots of things - it can’t be a prohibited animal, it can’t be from a prohibited part of the animal, it can’t be killed in certain ways, it can’t have died on it’s own, it has to be bled, and it can’t be prepared in certain ways.
e.g. For mammals, it should have cloven hoofs (no dogs, cats, pigs, etc.) and chew cud (cows, goats, sheep are ok) For birds, it shouldn’t be a meat or fish eater. For fish, it should have scales. There are several more rules for what animals are allowed.
Blood is prohibited, as are certain fats that surround certain organs. These were used in temple sacrifice.
There’s a specific rule that a goat shouldn’t be cooked in it’s mother’s milk. This is generally seen as a prohibition against mixing meat and dairy.
See Leviticus 11.