The inherent restrictions imposed by a forum such as this will impede a completely satisfactory discussion of your question, especially considering the very philosphical nature of the subject.
Having said that, an explanation of The Laws of Nature requires that you find yourself most comfortable in one of two camps. One being Humean, i.e., resting on the works of David Hume (recently retitled as Regularists) the other a Necessitarian. I'll suggest, for the sake of brevity, that you research the full implications of each.
However, some agreement is reached in at least five areas of describing a Law of Nature. All five rests on the pillars of Strength and Simplicity. They are strong enough to withstand critical scrutiny without the neccesity of adding layers of explanation or modification, hence Simple.
The five are:
1. Factual, not logical (I, personally, think a better adjective would be not intuitive, but that violates the dictum of simplicity)
2. Contain no proper names.
3. Are universal or statistical
4. Are conditional claims, not categorical ones.
5. Are true for every time and every place in the universe (this appears to me to be a corollary of #3, but with a distinctive difference, i.e., the addition of time as a consideration)
Contd.