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The paper starts burning because the power of the sunlight is coverged to one point so it make the paper burns
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Actually the magnifying glass is a convex lens, it is thicker in the middle and thinner at their end.
When the sun light passes through that lens, it converges the light and forms a real image of sun but very diminished. If you have done it practically, you have seen a point image formed on the paper.
To do burning we have to place the lens at a distance so that it will form the point image for some period of time.
That point image also have the heat energy as the sun, because it is actually the image of sun, so after a while that piece of paper starts burning.