Flight is an action in which a character leaves the ground and propels itself in the air. Many things can take flight, be it a plane or a man wearing a jet pack.
In the real world, man can not fly and must resort to machines to do so. The most common way to fly is via airplane. Airplanes are giant metallic tubes with wings. Each wing has a reactor attached to it letting the plane get enough speed to fly up and away. Thanks to the vessel's wings, planes can fly stably at high altitudes for long periods of time.
Another way to fly is via jet pack. Jet pack technology consists in bolting two reactors to a sort of backpack which lets an individual user fly up. Jet packs are uncommon in the real world mainly because they are dangerous and very experimental.
Video games let characters fly in ways that are not possible in the real world. Rocket boots are a popular example of this. Characters have rockets strapped to each of their legs and manages to fly around. This would not be possible in the real world as it would be very hard to make both rockets propel in exactly the same direction. Also, it would be impossible to fly anywhere but up.
Another popular way of flight in video games is via giant robot suits called mech suits. Said suits let the user fly anywhere, be it in the air or in space. These mech suits fly usually thanks to rocket boots (see above) and thrusters that are incorporated in the back of the suit.
Finally, when developers lack inspiration as to how to make a character fly, they just make him fly. This can be thanks to magic or super powers like Superman. Sometimes, characters can fly thanks to some kind of wacky object like a hat with wings on it.