(also known as the velum) is the soft tissue of the back of the roof of the mouth. You can feel it lift when you yawn, and how high or low it is can affect how your voice resonates when you sing.
As you can see in the graphic to the right, if your soft palate is lifted and connects to the back wall of your throat, then the sound and air will not go through your nose. If your soft palate is lowered, then the sound/air can go through your nose. If your mouth is closed, the sound/air will only go through your nose. If you plug your nose and have your soft palate lowered, the sound gets trapped in your nose and it will sound very nasal! Depending on what you are singing, you can lift or lower your soft palate to make it sound the way you want.