The Airlift Card allows you to transfer your armies long distances. Each time you play one, you can do a single transfer from any of your territories to any other territory of yours or one of your teammates. Similar to a normal transfer, those armies can't do any other action that turn. They must wait until the next turn to attack, for example.
One big benefit of the airlift card is that it happens before any attacks take place. Therefore it can be used as a way to sneak armies into a territory that needs immediate defense. Rarely, it can even be useful to use on territories that already connect anyway, simply because it's guaranteed to happen before any attacks.
Specifically, airlift cards happen after deployments, after Emergency Blockade cards, but before attacks and transfers. It's recommended to not abandon a territory on the same turn that you airlift to or from, as it will cause the airlift to fail.
In a fog game, players can see the airlift take place if they can see the army total on either the source or destination of the airlift. When a player sees one, they get to see both locations even if the other one is fogged.