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The fact that we live in this 'sea of air' is crucial to flight. Quite simply, the fluid nature of air is what allows us to use Bernoulli's principle to acheive lift. 

Air, like all fluids, follows certain principles: fluids forced through narrow spaces will speed up, and faster moving fluids will have less pressure. 

Air passing over the top of a wing will be forced through a narrow space, which speeds it up, and lowers its pressure. The air under the wing is undisturbed, thus it has more pressure. With more pressure ont he bottom than on the top of a wing, the plane is lifted up, even though it is heavier than the air that surrounds us.