The act of soaring through the air is flying. You can also use this word to describe anything that's soaring through the air, like a flying squirrel or flying insects.
Use flying for anything that flaps or flutters above the ground, from flying fish to flying turkeys. It's also good for describing things that are propelled or blown into the air: "As the baseball hit the window, I ducked to avoid the flying glass." "The wind picked up and I watched the flying leaves dance around my yard." Some things only appear to fly, like a flying buttress, an architectural projection that "flies" from the side of a building.