Why do Marine animals have fins.
It is more efficient to use fins than feet, hooves, or other similar body parts. It is the same reason that you can swim faster while wearing flippers. Having a larger surface area allows animals to push against more water, so that they have more force when swimming. Here is a picture of the bones in a dolphin fin. They are extremely similar to the bones in a hand, because dolphins evolved from land animals that had individual fingers.
Amphibians like frogs and salamanders have webbed feet, which is a "compromise" between feet and fins. These feet allow them to push against water with more power, since they have webbing instead is separate fingers. It also allows them to grip the ground on land, since their fingers can move independently of each other.
Dorsal fins also aid in stability. Many marine animals and mammals are fusiform (torpedo-shaped) to reduce drag in the water and make locomotion easier. Without fins for stability, primarily dorsal fins, it would be difficult for animals to orient upright in the water without rolling. The dorsal fin actually increases lateral drag (rolling side to side) to provide this stability. Check out this reference for more information