There's a beautiful book on the subject of aerodynamics, Stick and Rudder.
Either the book you are reading is not very smart about how airplanes work, or you are mis-reading it.
Normally, the way you turn an airplane is the same way you turn a bicycle, motorcycle, or high-speed boat.
You bank or tilt the vehicle in the direction you want to go.
Since you always have a lift vector of force coming up through the center of the vehicle, by tilting the lift vector you are using some of it to accelerate you to one side.
That puts you into a circular path.
(You see this in movies about flight, where the aces are constantly twisting and turning.)
You can turn an airplane without banking it.
If you keep the wings level and simply give it left rudder, that swings the nose to the left,
which presents the right side of the plane to the wind.
You feel this as a lateral force.
That lateral force does cause the plane to travel in an arc to the left.
However, that force is much weaker than if you simply bank the plane.
In fact that maneuver is called a skid, just like skidding an automobile.
There are violent maneuvers that require advanced training in which parts of the wing surface can be stalled, or some parts stalled more than others, such as spins and snap rolls.
Normal utility aircraft (non-aerobatic) have wings slightly angled upward (Dihedral angle)
In such a plane, if you simply apply left rudder and nothing else, that swings the nose left, and swings the right wingtip forward into the relative wind. Since it is angled upward, the wind gets "under it" and pushes it up, thus putting you into a bank.
So if you simply apply left rudder, the plane will bank itself, which is the better way to turn. (Also, a certain amount of sweep-back angle to the wings will do that.)
(Oddly enough, if you are in a negative-lift situation, like an outside loop or inverted flight, to turn left, in your personal reference frame, you need to bank right, which makes sense when you understand that the lift vector is reversed.)