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.
They're strong against the Bug type because in real life, birds are natural bug deprators.
They're strong against the Fighting type because it's difficult to hit something that's moving in the air.
They're strong against the Grass type because in real life, many birds eat leaves, fruits, roots, seeds or vegetables, and also because many birds live on trees. Besides, tornados and hurricanes destroy crops as well as trees.
They're weak against the Electric type because one of the biggest cause of bird death is that they get electrocuted while flying or with the poles. And because birds are mostly on the air, they don't connect with ground, which diverts electricity.
They're weak against the Ice type because in real life, birds don't resist cold temperatures, and that's the reason they migrate.
They're weak against the Rock type because in ancient times, people used hunted birds by throwing rocks to them, making them fall to the ground.
They're immune to the Ground type because something that is flying doesn't touch ground, therefore, they don't get affected by earthquakes and Earth shifts.