What has been explained just about covers it. I can only offer a practical example in an attempt to reinforce the principle.
Bear in mind that an aircraft in a balanced turn is yawing and rolling in the same direction (and also pitching a little too, but we can ignore pitch for our purposes at smaller angles of bank; it does become more significant in a steep or max-rate turn but that is not a relevant factor in this discussion).
I have an old radio controlled model slope soarer glider, a semi-scale model of a Breguet Fauvette. The model has a V tail with elevators only, working as a pair (only up or down in unison). It has NO steering rudder surfaces as such, simply because it was designed as a 2 channel model.
The full size aircraft had a control mixer giving the surfaces the ability to offer rudder as well as elevator - "ruddervator".
The aircraft model has long wings and full wing-length ailerons. Because of this arrangement, to make it turn properly, it really does need some "in-turn rudder" to give the necessary yaw into the turn.
By using conventional aileron travel (one up / one down), the RISING wing suffered more drag than the falling wing so the nose yawed OUT of the turn, such that the aircraft flew cross-controlled as it was rolling into the turn.
Adverse yaw is very noticeable on a long winged aircraft because drag changes on the outboard end of the wing give a large moment about the yaw axis.
This adverse yaw reduces the initial rate of turn, something not good in a fast slope soarer. Once the turn was established, (aircraft no longer rolling by application of ailerons), the adverse yaw stopped and the weather-cock effect took over, allowing the aircraft to maintain the turn reasonably well.
I had to adjust the ailerons linkages to become more and more differential until the aircraft is now controlled in roll ONLY by the aileron on the inboard side of the turn i.e. by using UP aileron only. The rising elevator does two things. It reduces the lift on the "inside" wing and it also causes DRAG on the "inside" wing, giving roll AND yaw in the correct direction for the turn. It flies really well now.
Do bear in mind that adverse yaw is a TRANSIENT effect only, when the aircraft is rolling due to the application of aileron.