A brown dwarf (BD) is a star-like object which has insufficient mass to sustain fusion (the HBMM for hydrogen-burning minimum mass) in the manner of main sequence stars ("stable fusion", i.e., of 1hydrogen), but with enough to trigger deuterium burning (the DBMM or deuterium-burning minimum mass). This is roughly (and standardized as) 13 to 75 Jupiter masses. They can have an effective temperatures ranging from 250 K to 3000 K, and any of the spectral classes, M-type star (M dwarf), L-type star (L dwarf), T-type star (T dwarf), or Y-type star (Y dwarf). They cool over the course of their life, so their classification evolves, which presents a mass/age degeneracy: that a young brown dwarf within the lower end of the mass range has an Teff (and spectral class) identical to that of more massive brown dwarfs that are sufficiently older.
The coolest main sequence stars are within the hotter end of the brown-dwarf range, and the classifications M and L can be hydrogen burning stars. Also, many planets are warmer than 250 K. Consequently, even with the spectral class and absolute magnitude determined, its mass is needed to determine whether the object is a planet, a brown dwarf, or a star. Thus, when candidates (substellar objects of some kind) are found at distant orbits from a star, so mass-determination is possible as well as spectrography from direct imaging, characteristics of such bodies can be collected, which, in turn, assist in classifying similar objects found nearer the stars, e.g., by transits. Modeling such bodies has the extra complication of the possibility of clouds in the atmosphere.
Star formation and planet formation theories are decidedly different: the prediction of brown dwarfs grew from the thought that sometimes star formation would not accumulate enough mass. Jupiter, our best example of a giant planet, is mostly hydrogen and helium (as is a star) but is presumed to have formed after the Sun, from the solar nebula. There may differences between such a giant planet and a failed star. Stars do often form in binary pairs and the fact that the object is orbiting a star is insufficient criteria.
The early-established observables used to identify brown dwarfs were the presence of lithium and/or methane (Main sequence stars generally burn their lithium early, thus it was a sign that the star never burned hydrogen). The first observed brown dwarf was identified as such in 1995. As of 2013, hundreds of brown dwarfs are known.
Brown dwarfs' rotation periods are generally hours, typical of a planet, rather than multiple days, typical of a star. They lack stars' phases of stellar wind, something that reduces angular momentum. Also, they grow smaller as they cool, causing their rotation to increase.
The mass criteria (13 to 75 Jupiter masses) is not a perfect match indicator of whether the object burns hydrogen, deuterium, or nothing: this also depends on the constituents of the object (i.e., metallicity). By other than mass criteria, it is thought that brown dwarfs may range from 10 to 90 Jupiter masses. The 13-75 range is at best suitable for quick or preliminary classification.
The terms black dwarf, planetar and substar were also used for in the 1960s/1970s for brown dwarfs before a consensus developed regarding the term.
(The term black dwarf is currently used for future white dwarves that have cooled to a much lower temperature.)