The reason lies in the structure of the eye itself. Nocturnal animals tend to have proportionally bigger eyes than humans do. They also tend to have pupils that open more widely in low light. So, at the outset, nocturnal eyes gather more light than human eyes do.
Many nocturnal animals have larger eyes than diurnal animals. This is so that their eyes can capture as much of the available light as possible to help them see in the dark.