A main-sequence star is a star powered predominantly by sustained hydrogen burning in its core. Hydrostatic equilibrium balances gravity with a pressure gradient, while thermal equilibrium approximately balances the nuclear energy supply with losses. The Sun is an example; a red dwarf is a cooler, lower-mass example.
Membership in the main sequence describes an evolutionary state, rather than simply small size or low luminosity. A white dwarf can be hotter and smaller while lacking sustained core hydrogen burning. Within the main sequence, a steep mass-luminosity relation makes massive stars consume their accessible fuel faster, so a larger fuel supply does not necessarily give a longer main-sequence lifetime.
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