Science is a powerful way to know about the world, but it has its limits.
The philosophy of science is the study of the nature and methodology of science. In this sense, it is a branch of epistemology.
What do we mean by "the study of"? A typical definition might be something like: "the branch of knowledge concerned with questions about the nature and methods of science." We can see how this fits within the broader scheme by looking at some other areas that fall under epistemology: logic (how are good arguments made?) and ethics (what makes something right or wrong?).