@Prometheus At AOPA I understand the definition of “behind the power curve” to be a little broader. I believe it refers to any airspeed where it will require more power to fly slower, instead of the usual less power to fly slower. This is typically any airspeed below Vx. On many GA aircraft it is possible to maintain straight and level flight at airspeeds below Vx; the slower you want to fly, the more power you will need.
It refers to the graph of drag vs. thrust and airspeed such as this: https://www.boldmethod.com/learn-to-fly/performance/vx-vy/. Practically speaking, when you are flying below Vx, it takes a lot more power to increase airspeed than when you are flying above Vx. That's because there's a lot more drag. In an underpowered aircraft there may not be enough power available to overcome drag and your only chance of increasing airspeed is to lower the nose. Propeller efficiency can compensate for lack of engine power to some extent but not when there is a severe lack of power vs. drag. A go-around is a good example of being behind the power curve. You are flying slowly because you intend to land. Drag is high because airspeed is slow, flaps are deployed and maybe you have gear lowered on a retractable. Power and thrust are low because you are landing and don't want to float. Then you decide to go-around. It takes full power to increase airspeed even modestly and start climbing until you get to Vx. Then you can start to reduce drag by raising gear and flaps (also reduces lift), which increases airspeed significantly.
@James Mayhew I meant to say Vy, not Vx, in this post. @Andrew Meranda Nice link and graphic of power required and power available curves.
@Andrew Meranda I think you made a typo in this sentence: “when you are flying below Vx, it takes a lot more power to increase airspeed than when you are flying above Vx.” The power curve shown in the link you provided shows that at low airspeed, say Vx, the power required to fly a little faster - say, Vx + 5 kts - is actually lower . As I think we agree, that's what “behind the power curve” means.
Please note that I am referring to the power required to fly at that higher airspeed after you have accelerated to that airspeed. In order to accelerate from Vx to Vx + 5 kts - without descending - you would have to increase power and gently push the nose down to maintain altitude. Once you reached Vx + 5 kts, you would reduce power to stop accelerating and maintain this airspeed. This power setting would be lower than it was for Vx - rough guess 50 - 100 RPM less.