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The rudder operates the aircraft around the yaw axis, think of it as a vertical axis through the centre of the fuselage. This is a slightly different axis of flight since it isn't solely used to achieve a climb / descent or roll (strictly speaking) by itself like the elevators (lateral axis) or the ailerons (longitudinal axis).
The rudder (therefore, yaw) can be seen to used as a secondary function to the elevators / ailerons.
When banking the aircraft, to fly in balance i.e. not side slipping the aircraft into the relative air flow you will need to add rudder. This makes your turn coordinated. When flying straight and level, you may need rudder to fly coordinated. When making power changes, you will need rudder due to the slipstream (single engine props only) affecting yaw.
So in short, to start a turn, you will use ailerons. To keep that turn in balance and to keep that aircraft in the turn and not skidding out or slipping in, you use rudder.
To try and bank the aircraft using rudder alone is wrong.
To complicate things a bit further, both the ailerons and rudder have secondary effects. Ailerons induce roll and then yaw and rudder induces yaw and then roll. Balancing them both is the key.