Science operates on the principle of methodological materialism, which means that science can only study the physical universe. Popularly though, science is often misappropriated and misrepresented to promote philosophical materialism, the unverified belief that the physical world is all that exists.That basically hits all the bases.
Science is dedicated to only making judgements on things it can measure quantifiably. You can't measure the supernatural, not directly, and attempts to measure it indirectly, like the double blind studies about the effectiveness of prayer, are often treated with skepticism as well. Now this dedication to the physical and measureable is a good thing as a whole because resorting to theology to explain how something happens is usually a dead end. Think about it, can't "God did it" be the answer to every question in one way or another? And once you conclude that God did it, going any further is not a matter of physics but meta-physics. You transform science into philosophy and theology.
However there are people that talk about science as if it proves that God doesn't exist or that there is no supernatural. Science proves philosophical materialism as it were. This is circular reasoning at a fundamental level. If the supernatural is not an allowable conclusion, then your results will never conclude that an event is supernaturally caused will they? This is the case even if the event in question was the result of direct divine intervention. So even if the supernatural is the right conclusion, science isn't allowed to make use of it.