Airplanes have a problematic relationship with fuel: The more fuel they take on board, the heavier the plane is (and the less weight capacity it has to carry other things at launch). Eventually there is a point of diminishing returns, where planes are basically burning fuel to carry fuel. Enter air refueling.
As a concept, air refueling is both simple and crazy. It entails figuring out a way to get fuel from one aircraft to another, while both are flying. Early attempts at this method were downright insane, involving wing-walking with a can of fuel. While this actually worked, it was not exactly efficient, though it did help set distance records in the early days of flight.
As the technology advanced, it became clear that a gas can wouldn't carry enough fuel to make the maneuver worthwhile, so various methods using hoses and special attachment points were developed. For decades now, air refueling has been routine for military flights, and is the only way to make certain missions possible, given the range of a given airplane and the limited set of places it could safely land and refuel. Fortunately, we've gotten really good at this.
In this short video, Sploid shows us archival footage of the progress of air refueling. If you ever wondered what it looks like to gas up your jet in midair, behold!