Same way anything flies faster than the object that hit it: it compresses and springs off the bat. The baseball deforms, allowing it to absorb some of the kinetic energy from the bat and turn it into physical potential energy, over a slightly longer time frame than if it had been more rigid like a bowling ball.
Once it fully deforms, it starts to move at the same speed as the bat, but since the bat’s not imparting any more energy, it starts to decompress. The movement of the bat and the decompression together send it flying a little more quickly than it would as a perfectly solid ball.
*This is the same reason aluminum bats are more powerful– they have much more spring than wood, so the effect becomes twofold.
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