Physicists classify both liquids and gases as fluids, based on how they flow. Even though air, water and pancake syrup may seem like very different substances, they all conform to the same set of mathematical relationships. In fact, basic aerodynamic tests are sometimes performed underwater. To put it simply, a salmon essentially flies through the sea, and a pelican swims through the air.
The core of the matter is this: Even a clear sky isn't empty. Our atmosphere is a massive fluid layer, and the right application of physics makes it possible for humans to traverse it.