To soften is to make something soft, or to become soft. A stick of butter will soften after sitting on the counter for an hour—or you can soften it by squishing it with a wooden spoon.
You can literally soften things, the way a sculptor softens clay or you soften the skin on your hands with lotion. Turning down the sound is another way to soften something: "I'll soften the radio so it doesn't keep you awake." When you make something gentler or less severe, you also soften it, like when a lawmaker tries to soften the effect of a law by proposing a tax cut in return.