Cat flaps are often placed in windows or doors to allow your cat (or dog) to get outside without you needing to open and close the door. Good flaps will even have locks which will allow you to lock your cat in our out.
The cat flap pictured has a lock that will lock one way - cats can come in, but can't go back out. This is great when it's later in the afternoon and the cat needs to stay inside.
Absolutely not. Our cats are indoor only, but even if they were allowed outside, we would not install a cat door. With all the wildlife in our area it would be like an open invitation. I don't need squirrels, snakes, mice, or anything else that belongs outside, in my house.
I don't have a cat flap but my parents do. It's really handy. Although the cats that use the cat flap have been known to run into it - even when it's locked. While it's funny, it's also kind of embarrassing.