The Kirchhoff’s first law $(\sum \mathrm{i}=0)$ and second law $(\sum \mathrm{iR}=\sum \mathrm{E})$ where the symbols have their usual meanings, are respectively based on -

Kirchhoff's first law is based on the conservation of charge because sum of current entering to the junction is equal to sum of current leaving the junction. Kirchhoff's second law states that the algebraic sum of potential drops in a closed circuit is zero. So, it is based on the conservation of energy.