A more massive main sequence star is more luminous primarily because it is bigger. The larger core contains more photons and more thermal energy. Calculations using these principles reproduce the observed mass-luminosity relation. The mass of a main sequence star determines its radius and its luminosity. The mass of a main sequence star determines its position on the HR diagram.
Stars lie on a narrow sequence because luminosity and temperature climb steadily with mass.
A main sequence star is a star that is sustaining its luminosity by fusing hydrogen into helium in its core. Hydrogen fusion can sustain a star for a long time, which is why most stars are found on main sequence. However, it does not evolve up or down the main sequence. Eventually, the supply of hydrogen in the core runs out. At this point, the star begins to evolve much more rapidly.