Natural law: The notion that events and things in reality can be explained in terms of universal generalizations that refer to invariant aspects in reality.
It seems the idea started in analogy with laws in society: God commanded or Nature was organised such that all things of kind X if in circumstances Y have property Z.
Indeed, as far as language is concerned, and its human use to explain things this way, this makes sense. The problems start when one inquires whether indeed this is true: Are there in reality things X, Y, Z such that it is true that all things of kind X if in circumstances Y have property Z - always, everywhere, without exception? And if this is true for some things, is it necessarily true or does it just happen to be so, always and everywhere? And if such statements of natural law are sometimes necessarily true, in what sense? And if there really are natural laws in any of the above senses, are all things fully describable by some natural laws, or are there exceptions - say chance?
A further complication arises with quantum mechanics, that assumes that there are certain natural processes that produce chance events, that cannot be predicted with certainty. Linguistically this requires only a small change: Are there in reality things X, Y, Z such that it is true that all things of kind X if in circumstances Y probably have property Z - but then the same questions may be posed as before. And further questions arise about probability and how to establish it, which indeed also apply apart from chance events, namely in case of ordinary statistics.
In any case, and whatever the answers, science is based on the notion that there are natural laws of some kind, and that they are true because some features of reality are invariant.