To cling is to tightly grasp something or to stick closely to something, like how wet clothes cling to the wearer.
Clinging has to do with closeness. A scared child will cling to his parent, holding on tight. People in love cling to one another in embraces. When you're on a roller coaster, it's best to cling to whatever restraint you can. Similarly, things cling to each other when they're hard to separate. Clothes fresh out of the dryer often cling to each other. Strands of cooked spaghetti cling to each other. Stretchy clothing like spandex clings to the bodies of the people who wear it.