What´s the logic behind the Power Curve? Aircaft thrust is what counteracts drag, but in flight school they tought us that propeller aircraft are &quot;power producers&quot; and not thrust producers as jets. (That´s because the propeller needs the power of the engine to rotate and generate thrust, while a jet engine generate it by itself).
In both cases we can look at the thrust curve to get some performance information, but for props, we need to get a power curve also (get it multiplying thrust times airspeed values of the thrust curve) to get other performance features as Vy. (found where greatest excess power is).
I can´t understand the logic behind that, I mean, why does power affect airplane´s aerodynamic? Why is it important how much power does the engine has if what really makes the aicraft move forward or climb faster is thrust?
why does power affect airplane´s aerodynamics?

It doesn't. The aerodynamics will determine how much excess power is left for acceleration or climb. But not the other way around.

Why is it important how much power […] the engine has?

Because the power of a piston engine is constant for the same air density, regardless of speed. It is more helpful to give a power rating because that figure is valid over the whole speed range, unlike thrust. Thrust is inversely proportional to speed and so a thrust figure is only valid for exactly one operating point.
Pure turbojets have approximately constant thrust at subsonic speed, so here the thrust rating is more useful. The power a turbojet can produce increases with flight speed.