The main sequence of the Hertzsprung-Russell diagram is the curve where the majority of stars are located in this diagram. Stars located on this band are known as main-sequence stars or dwarf stars. The coolest dwarfs are the red dwarfs.
This line is so pronounced because both the spectral type and the luminosity depend on a star's mass only to zeroth order as long as it is fusing hydrogen -- and that is what almost all stars spend most of their "active" life doing.
At closer inspection, one notices that the main sequence is not exactly a line but instead somewhat fuzzy. There are many reasons for this fuzziness, the most important one still being observational uncertainties which mainly affect the distance of the star in question but range all the way to unresolved binary stars.
But even perfect observations would lead to a fuzzy main sequence, because mass, after all, is not the only parameter a star has. Chemical composition and -- related -- its evolutionary status also move a star slightly on the main sequence, as do close companions, rotation, or magnetic fields, to name just a few. Actually, there are very metal-poor stars (subdwarfs) that lie just below the main sequence although they are fusing hydrogen, thus marking the lower edge of the main sequence's fuzzyness due to chemical compositon.
Astronomers will sometimes refer to the zero age main sequence or ZAMS. This is a line calculated by computer models of where a star will be when it begins hydrogen fusion.
Stars usually enter and leave the main sequence from above when they are born or they are starting to die, respectively.
Our Sun is a main-sequence star - has been one for about 4.5 billion years and will continue to be one for another 4.5 billion years. After the hydrogen supply in the core is exhausted, it will expand to become a red giant.