* The Moon is much smaller than the Sun, a star. The Sun is a giant ball of burning gas, and the Moon is a rocky sphere.
* From Earth, the Moon appears larger than the Sun. This is because the Moon is much closer to Earth than the Sun.
So, the answer depends on what you mean by "bigger."
* In terms of size: The Sun (a star) is much bigger than the Moon.
* In terms of apparent size in the sky: The Moon appears larger to us than the Sun.