A first principle is a foundational assumption or proposition that cannot be derived from other assumption or propositions. By attempting to break down problems into first principles and re-constructing solutions using these building blocks, you're less likely to be biased by prior assumptions. This in turn can lead to more innovative solutions.
A child repeatedly asking "why?" to answers for an initial question is intuitively thinking in first principles.
A company buiding an in-expensive product by investigating ways of using the raw materials firsthand instead of just following existing conventions.