Total Aircraft Drag is the sum of Induced Drag and Parasite Drag. Induced Drag reduces with (the square of) speed whereas Parasite Drag increases with (square of) speed. If we plot this we get a somewhat U shaped curve for Total Drag at different speeds.
If we draw a horizontal line representing a particular Drag value - Except for the lowest point on the curve, representing the least Drag point, every other point above lowest Drag on the Drag axis of this curve corresponds to 2 points on the curve, ie corresponds to two speeds. Since Power is proportionate to Drag, every Power setting corresponds to 2 speeds except at the lowest point on the Drag curve.
So, as speed increases in flight, the airplane could accelerate to, and maintain the first/slower speed, or further accelerate using available Power till it reaches the second/higher speed value.
Typically we would not want to fly at the lower of the speeds when the same power can give us a higher speed.
"Why does power help us maintain altitude in slow flight?" - actually, the forces and force couples at play are the same whether high speed or low, but from the the dynamic stability point of view, low speed and high speed differ as follows - lower speed lies in the zone of dynamic instability in speed, ie any drop in speed results higher Drag thus tending to naturally reduce the speed further unless Power is added to the equation. If power cannot be added, the only option is to push the nose down and trade altitude for speed (provided ground contact is not a factor!). Due to the shape of the curve, any hesitancy in taking the counter-action would result in a rapid speed loss requiring more and more power. This is commonly referred to by pilots as "the wrong side of the drag curve". Compare this to the right side/higher speed zone, where a drop in speed would result in lower Drag thus naturally tending to return the airplane to the desired speed without much by way of a Power input.
Similarly, for completeness of understanding, you may like to figure out in your mind, the dynamics of what happens when there's a slight increase in speed.