Bats' wings and legs have a unique structure. They can lock their feet to a support and suspend their bodies down, without the fear of falling. In this mechanism, the bats open their claws (like you would hold your fist open), then find a support to grip to (like you would hold an object in your clenched fist).
There's something else that helps bats take quick flight. And it is, yes, their hanging upside down! How does it help? In the upside down posture, it's easier for the bats to take flight by just dropping themselves down and gliding. They cleverly use the gravitational pull to their advantage by dropping from a height to take flight.
Imagine a tired you hanging down from a support. No, that wasn't a joke. It was meant to help you realize how you would feel then. Won't you feel a relaxing stretch in your body? That's how bats feel!