For example, noticing that the sun follows a predictable pattern in the sky over the year is not science, because it comes with no explanation and no prediction of anything else.
Similarly, learning swordmaking through trial and error is not science, it is a ritual. Figuring out why the steps in making a sword work, and thereby being able to modify/apply it elsewhere, is science.
In other words, science is the application of the scientific method.
Religious explanations are not scientific, as they are based on faith, not experiment.
Mathematics is not science, either, that's why we say "science and mathematics". Mathematics is a tool for describing phenomena. Math can be used to describe the path of the sun in the sky, but it doesn't explain it.