A dwarf star is a star that is not a giant or supergiant … in other words, a dwarf star is a normal star! Of course, some dwarf stars are much smaller (less massive, have a smaller radius, etc) than normal (or main sequence, not really massive) stars … and these have names, like white dwarf, red dwarf, brown dwarf, and black dwarf. Our very own Sol (the Sun) is a dwarf star … a yellow dwarf.
Looking more closely at this rather confusing class of objects: a dwarf star has a mass of up to about 20 sols, and a luminosity (a.k.a. intrinsic brightness) of up to about 20,000 sols (‘sol’ is a neat unit; it can mean ‘the mass of the Sun’, or ‘the luminosity of the Sun’, or …!). So just about every star is a dwarf star! Why? Because most stars are on the main sequence (which means almost all have luminosities below 20,000 sols), and only a tiny handful of main sequence stars are more massive than 20 sols. In addition, once a star has burned through all its fuel, it becomes a white dwarf (and, one day, a black dwarf), all of which are dwarf stars by this definition.
The most interesting class of dwarf star is, perhaps, the black dwarf star; it’s hardly a star at all (it doesn’t burn any fuel, except, perhaps, deuterium, for a few million years or so).
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So why do astronomers have this classification at all? Hitting the history books gives us a clue … back when spectroscopy was getting started, among astronomers – and well before there was any kind of astronomy except that in the optical (or visual) waveband; think the second half of the 19th century – a curious fact about stars was discovered: the spectra of stars with the same colors could still be very different (and when their distances were estimated, these spectral differences were found to track luminosity). So while dwarf stars overwhelmingly dominate, in terms of numbers, the giants (and sub-giants, and supergiants) pretty much rule in terms of what you can see with your unaided vision.
Neatly linking one kind of dwarf (the Sun, as a yellow dwarf) to another (white dwarf) is Universe Today’s The Sun as a White Dwarf. Other Universe Today articles on dwarf stars (not only white dwarfs!) include Astronomers Discover Youngest and Lowest Mass Dwarfs, Brown Dwarfs Form Like Stars, and Observing an Evaporating Extrasolar Planet.
Astronomy Cast’s episode Dwarf Stars has more on this topic.