Great question! The term 'pack' usually refers to a small or medium size group of animals, but beyond that the term is somewhat vague. Animals have a variety of social structures -- species can be completely solitary (e.g., great white sharks), form complex societies (e.g., gorillas, ants, humans) and everything in between. Frequently groups of animals that form small to medium sized groups that we would consider a 'pack' are based around family units. Sometimes, these small groups are comprised of two parents and their children (such as a wolf pack). The parents are the natural leaders of the pack because the offspring need protection and the pack stays in it's configuration until the young wolves grow up.

Sea lions are an alternative 'pack' structure- there is one dominant male that controls a harem of females (which are his mates) that he protects/guards against other males. 'Leader' probably isn't as appropriate so much as 'dominant', but the reason the male controls the group (rather than some other male or one of the females) is due to his larger physical size and aggression.

The last example I'll give is that of an honey bee colony, one of the most elaborate social structures. The queen bee lays eggs which hatch and become her sterile worker daughters. The workers do everything: forage for food, defend the nest, and raise up new workers. These workers are bound to the colony via chemical pheromones, and those chemical smells are how the workers recognize the queen. However, the queen doesn't lead her colony by 'telling' them what to do. Their collective behavior is an emergent property of many distinct individual actions, but it's their instinctual response to these chemical signals that result in it looking like the queen is the 'leader'. The worker daughters instinctually protect their mother, the queen, and when it's time to find a new home they form a swarm surrounding the queen and move in mass. Despite the appearance that the queen is in charge, however, it's actually the workers that decide where they should next call home & it's a democrat process based on votes by scout bees.

I'm not totally sure we know that in many cases. Wolf packs are families, so the pack leader is probably the most senior member of the family, basically the head of a household that humans would have. Lion prides are led by the most physically intimidating male. I don't know what the hierarchy there is in flocks of parrots or crows, if they even have something like a pack leader.