Pokémon of this type can fly, many of them live at high altitudes, even. Most of them are birds and insects. Their power is mostly related with aerial and wind-related attacks. Most of them have wings, but there are also some of them that just float without wings, like Rayquaza and Gyarados.
The Flying type is the only existing type that is combined with every other Pokémon type, making this type the most varied.
Famous Flying-type Pokémon Trainers include Falkner, the first Gym Leader of the Johto region; Winona, the sixth Gym Leader of Hoenn; and Skyla, the sixth Unova Gym Leader.
They're strong against the Bug type because some birds eat bugs like worms.
They're strong against the Fighting type because Fighting Types represent humans, and how we were limited to mastering the ground until the invention of the plane.
They're strong against the Grass type because tornadoes and such can tear up trees.
They're weak against the Electric type because while in the air, they don't make contact with the ground, so they can't divert the electricity, so they're susceptible to strong electrical currents and it's easy for a thunder to hit something that's flying.
They're weak against the Ice type because birds will migrate in the winter.
They're weak against the Rock type because stones are used as projectiles in slingshots which were a common tool for killing birds.