This paper investigates the electronic states of graphene nanoribbons with zigzag and armchair edges, focusing on their band structures and boundary conditions. The finite width of these nanoribbons leads to an infinite set of bands, which can be understood using the Dirac equation with appropriate boundary conditions. For zigzag nanoribbons, the boundary condition allows for particle- and hole-like bands with evanescent wavefunctions confined to the surfaces, which turn into zero-energy surface states as the ribbon width increases. For armchair edges, the boundary condition results in admixing of valley states, leading to metallic behavior when the ribbon width is divisible by 3 and insulating otherwise. The study compares the wavefunctions and energies from tight-binding calculations with solutions of the Dirac equations, showing quantitative agreement for all but the narrowest ribbons. The results highlight the importance of the continuum description of graphene in analyzing the electronic properties of these nanoribbons.This paper investigates the electronic states of graphene nanoribbons with zigzag and armchair edges, focusing on their band structures and boundary conditions. The finite width of these nanoribbons leads to an infinite set of bands, which can be understood using the Dirac equation with appropriate boundary conditions. For zigzag nanoribbons, the boundary condition allows for particle- and hole-like bands with evanescent wavefunctions confined to the surfaces, which turn into zero-energy surface states as the ribbon width increases. For armchair edges, the boundary condition results in admixing of valley states, leading to metallic behavior when the ribbon width is divisible by 3 and insulating otherwise. The study compares the wavefunctions and energies from tight-binding calculations with solutions of the Dirac equations, showing quantitative agreement for all but the narrowest ribbons. The results highlight the importance of the continuum description of graphene in analyzing the electronic properties of these nanoribbons.