I never heard of "first principles" until Elon Musk used it. (Not a native English speaker) Now I see it everywhere. Must be the new overhyped term. "We start from first principles, just like Elon Musk". After looking at Google trends, I might be wrong, so nevermind ;) https://trends.google.com/trends/explore?date=all&q=First%20...
When we say a model is a first-principles model, it means it is derived through fundamental equations like conservation of mass/energy, and other known relationships. This is in contrast to a data-driven model, where the underlying phenomena are not explicitly modeled -- instead the model is created by fitting to data.
Elon Musk became associated with it because he applied this form of thinking to business problems, i.e. by establishing the "fundamental equations" (as it were), questioning some basic assumptions and coming up with conclusions that are necessarily true but that no one else has arrived at.
Data-driven models (or the human equivalent: reasoning by analogy) are convenient to build and work well in the space the data has been collected in (~interpolation). However, they do not extrapolate well -- you cannot be sure they will work outside of the space of training data that the model has seen.
First-principles models (or the human equivalent: reasoning by principles) are generally more difficult to build and test (I worked on first-principles physics models for a decade -- they are a pain), but because they are built on a structure of chained principles/truths, they often extrapolate well even to areas where data has not been collected.
This is why if you want to improve efficiency and operations in known spaces, you use data-driven models (fast to build and deploy, accurately captures known behavior).
But for doing design and discovery (doing new things that have never been done before), first-principles models/thinking will carry you much farther.