That's how it turns. It diverts the lift from vertical to the direction of the turn. That sideways component of lift is what turns the airplane.

All aircraft maneuver in basically the same fashion. There are three movable surfaces on the aircraft. These are the ailerons, vertical stabilizer, and horizontal stabilizer. In coordinated flight, the pilot in command will ideally use all three to effectively maneuver the plane. The ailerons are part of the wings. They are moving parts that alternately move either up or down, deflecting air to roll the plane to the right or left. The vertical stabilizer and the horizontal stabilizer are both located on the tail of the plane. The horizontal stabilizer, also known as the elevators, deflects air by moving up or down, just as the ailerons. It controls pitch, moving the nose of the aircraft up or down. Lastly, there is the vertical stabilizer, usually called the rudder. This moving part swings to the right or left, and controls the yaw of the aircraft. It is capable of moving the nose either left or right. With this said, one does not turn the aircraft by just pushing on the rudder pedal or turning the yoke to activate the ailerons. The key is that you use both, and often the elevators as well. If you think of the plane on a sea of air, the most aerodynamic way to make a turn is to roll the aircraft to one side or another. The lift from under the wings provides the primary force for the turn. This is also the key to maintaining maximum amounts of smoothness and control. Making these turns is a matter of coordination and ability to follow instruments. Lets take a real example: We'll start a flight in the 757. Shortly after liftoff we will most likely have to make one or more turns as ATC guides us onto our course. If I want to turn right to change headings, I would do the following. I will simultaneously give a gentle right turn to the yoke while also applying a small amount of right rudder. Depending on whether we are maintaining an altitude or in a climb, I may have to provide some elevator input. If I were to turn without banking, I would have to use the rudder only. The passengers would probably suspect something was wrong with the plane immediately. If I applied full right rudder, the plane would swing violently to the right and a cockpit alarm would most likely go off. The real purpose of the rudder is not as much turning as it is stability. If I was flying and the aircraft was suddenly hit by hard turbulence and knocked from its path, I might realign and stabilize by a short alternate input to the rudder pedals. So to summarize what I've said, aircraft really bank to turn in order to provide the smoothest and most aerodynamic maneuverability. Banking uses the acting force of lift under the wings to turn the plane.

It also keeps the G-force perpendicular to the wings which keeps the plane from sliding sideways or losing lift. Keeping the G-force perpendicular also helps the passengers maintain proper sense of attitude relative to the cabin. Usually you will only feel an apparent change in force or 'gravity' but not feel tippy. In a ideal, proper turn, a glass sitting on the tray-table will not slide and the liquid level in the glass will not tilt. Some stunt pilots can do a complete barrel roll with a glass sitting on the dashboard and not spill it.

Same reason motorcycles do and the same reason cars have sway bars and four tires. Gotta offset the inertia that would be keeping you going in the same line. In an aircraft it's diverting some vertical component of lift to go that-a-way. The turn also has some up elevator to offset the loss of lift and increased g-force in the turn, ih and little kick the rudder to point the nose, those motions are less drastic and less noticeable.

12-08-2016 Now picture this: If a plane turns without banking, the wind speed across the wing at the inside of the turn is less than the wind speed at the outside of the turn. So there is a natural tendency to bank into the turn, and you have to fight nature to keep the plane level. You also run the risk of losing lift entirely on the inside wing, and that causes a self perpetuating condition called a spiral. A spiral tends to be fatal. It's not nice to fight with nature.