What does laws of nature and of nature's God mean?

Laws of nature are "descriptive": we observe a consistent rule being followed.

Science understands it's ability to obtain knowledge is limited and can not without good reason attempt to assert intention. If things can be sufficiently explained with out such features as intention, than it would be an error to include said features. Things we fail to account for are investigate and tested.

"nature's God"... This might simply mean the "will of God"?

If you mean laws that God had made, then the laws are "prescriptive": prescribed intentional like our traffic laws. A believer might see "laws of nature" as their God's prescribed laws. Coming to this conclusion by either tradition, authority, revelation, and/or faith that the observed laws were intentionally created by their God.

Perhaps you mean, nature is God? This is a form of pantheism or panentheism.

Pantheism is the belief that everything composes an all-encompassing, immanent God, or that the universe (or nature) is identical with divinity. Pantheists thus do not believe in a personal or anthropomorphic god.

Panentheism means "all-in-God", and was formally coined in Germany in the 19th century in an attempt to offer a philosophical synthesis between traditional theism and pantheism, stating that God is substantially omnipresent in the physical universe but also exists "apart from" or "beyond" it as its Creator and Sustainer. Thus panentheism separates itself from pantheism, positing the extra claim that God exists above and beyond the world as we know it