The eyes of animals and humans have high-density rods that determine how much one can see in the dark. The ancestors of dogs and cats spent their days roaming the wild in search for prey. Their sense of vision has evolved to make them excellent night hunters. The high density of rods in their eyes makes them see more clearly in dim light. The abundance of rods enables them to see normally with as little as 15% of light than what we normally need to see clearly in the dark.
The pupils of a dog or cat also dilate significantly when there is a need to take in extra light. Cats have exceptionally large pupils and have outstanding night vision.
However, it is NOT true that cats and dogs can see well in pitch darkness. They still need some light in order to see properly.