Cat's curiosity can be explained by the fact that cats are predators and they need to be constantly aware of the food supply availability.
They have a very strong instinct to investigate everything that moves or makes noises, they investigate beyond open doors, cupboards, areas beside plants or cardboard boxes.
Curiosity is also the way to find the best shelter, especially for pregnant cats.
The need to explore is also due to cat's sensory systems, better than most other mammals'.
Cats have 30% more sensory tissue designed for detecting odors, as compared to humans.
The ears are very mobile and they are able to detect sounds at frequencies 50% higher than dogs can and the eyes don't have much capacity of distinguishing colors, but they can perfectly detect movement; cat's eyes can dilate so much in order to be able to make use of all available light.
To cats, a dark night is more like a dim day.
Cat's curiosity refines its sense abilities, bringing them up to their full functionality.
When a cat reaches the maturity, it also gains additional qualities that are not quite easy to understand by us, humans.
For example, the ability of finding the way back home even if they've never seen how they got there, there are some cases when cats got trapped in cars and had to return home from great distances.
Cats are able to return home even when their home is at a distance of 10 miles.
Well, it doesn't happen in a day, but most important is that they finally reach their home after a while.
The only explanation specialists found involves the magnetic fields.