I was cleaning out my photos and found this gem from last summer. My daughter had discovered this phenomenon and came running to find me. "Look, Mommy! The balloon sticks!"
Of course the balloon is not actually sticky. Why is it hanging there? Gravity is pulling it down.
Before thinking about what is happening vertically, think horizontally for a moment, into the picture (the y-plane in three dimensions). The fan blades are pushing air away from the camera, and pulling the air into the fan. The balloon is pulled along with the air, but cannot enter the fan because of its size. It is pulled against the grid of the fan. Wherever it touches the grid of the fan, there is a normal force and friction. Friction always works against motion. To whatever degree the balloon would fall due to the gravity, the friction holds it in place.
Of course I didn't lay all that on my three-year-old. Just part of it, I couldn't help myself. Mostly though, I'm just happy that she notices these things.