Animal products sit at the top of most countries' restricted lists. Fresh meat, unpasteurized dairy, and eggs are prohibited or heavily restricted almost everywhere because of disease risks like foot-and-mouth and avian flu. Processed and shelf-stable items are judged case by case: some countries allow commercially sealed, cooked products from approved origins, while biosecurity-strict destinations ban practically everything of animal origin, including jerky, sausages, ghee, and pet food.
Pet food is a commonly overlooked one; even sealed kibble contains animal ingredients and is often refused or requires certification.
The safe approach is to declare every food item without exception. Declared items that turn out to be prohibited are usually just confiscated with no penalty, whereas undeclared ones can bring hefty fines. Rules differ enormously between countries and even change based on current disease outbreaks, so look up the destination's agriculture or quarantine authority shortly before you travel rather than relying on what was allowed a few years ago.