Why does the pilot tilt the outer wing of the airplane inward while taking a turn?
Airplanes have two control surfaces involved when turning, the ailerons are on the trailing edge of the wings. By moving them in opposite directions, one up one down,the plane tilts, the lift the wings are generating now causes the plane to turn instead of going up. The rudder which is vertical at the back turns the plane to the left and right,but the rudder alone can turn the plane but not change it's direction (sideslipping) so in order to turn correctly you must use both the rudder and the ailerons.
sorry if that is unclear
The Aileron controls on the tip of the wing controls the rotation or bank angle of the a/c. If you want the LEFT wing do go down and RIGHT wing to go up, then the controls on the LEFT wing will pivot up and the Right aileron will pivot down. When the aileron rotates down, that puts more curver into the wing and creates more LIFT, so that wing will come up. The opposite wing will receive the Opposite input and move in the opposite direction.
So just before a turn, you will see the outboard wing time controls move. On larger airliners, there are also controls closer inboard on the wing that pop up and then drop back down. These are spoilers that distrub the airflow to kill the Lift on that wing, thus allowing it to drop.
Why does the aircraft rotate or Bank during a turn?
There are several reasons to rotate the aircaft to the LEFT when making a turn to the LEFT. First it is more comfortable on the passengers. If the a/c did not rotate and just turned left using the rudder, the passengers would be pushed to one side by te centrifugal forces---as well as their drinks and luggage, etc.
The aircraft banks and this keeps the forces acting directly through the passenger's seat of his pants. The only thing he feels is that he is slightly sinking into his seat.
Also, the aircraft is a little easier to control in a turn if it is banked. Different controls surfaces are used and this mades the turn easier. If the aircraft is a fighter jet making a high-speed turn, then it is better to rotate the a/c and use the tail controls that pitch the a/c up. The aircraft can pitch up more with these tail controls than simply turn using the Vertical Rudder.