Indulge me with this simplistic explanation:
Picture a bell curve that represents sound level during a musical passage. Now picture placing your hand at the top of the curve and pressing down. By "compressing" the curve, you are reducing the difference in sound level between the quietest and loudest passages; thus, the loud passages are not as loud. You have "smoothed out" the curve.
But the width of the curve has not changed, so the length of the passage is the same. If we raise the overall volume, but keep compressing the curve, the effect is a ringing note will sustain at a near constant volume without going beyond the top of the compressed curve. Electric guitarists in particular like this effect to be able to hold long notes.
Another real life example comes from our church. Years ago we had a pastor who was a bit on the charismatic side. He would go from almost whispering to shouting at the top of his lungs during a sermon. Being mic'd up, he drove the sound team crazy and made babies cry until they put a compressor on his channel. They could turn up the volume enough to hear him speaking softly, but when he cut loose with shouting, it didn't rattle the steeple.
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