All else being equal a more powerful amplifier provides:
The ability to play music at louder levels without losing response linearity or introducing clipping and strain distortion.
The ability to maintain relative volume level going from a smaller room to a larger room and a greater distance from the listening position.
The ability to maintain a relative volume level and dynamic headroom going to a speaker with less efficiency and more difficult to drive.
The ability to provide more relative volume and dynamic headroom (ability to be heard above louder levels of room background noise and din).