When the pilot moves the controls forward, the elevator surface is deflected downwards. This increases the camber of the horizontal stabilizer resulting in an increase in lift.
The additional lift on the tail surface causes rotation around the lateral axis of the aircraft and results in a nose down change in aircraft attitude. The opposite occurs with an aft movement of the flight deck controls.
Ailerons control roll about the longitudinal axis. The ailerons are attached to the outboard trailing edge of each wing and move in the opposite direction from each other. Ailerons are connected by cables, bellcranks, pulleys, and/or tubes a control stick.
Devices that aerodynamically change the wing and the Lift created by it cause other forces and effects to be created:
Secondary Effect of Elevators
Secondary Effect of Ailerons
In this example the aircraft has been rolled to the Left:
Secondary Effect of Rudder
To cancel out a the secondary effects and perform a smooth turn, we need to apply multiple flight controls at once!
Therefore a coordinated turn requires a small amount of Rudder towards the direction of the intended turn, in this case to the Left