A brown dwarf is an object larger than a planet but smaller than a star. The standard definition is that a brown dwarf is between 13 and 70 Jupiter masses. (Or:between .013 and .7 Solar Masses) Below 13 Jupiter masses, it is just a big planet. Above 70 Jupiter masses, it is a very small red dwarf.
What separates a brown dwarf from a planet, is that it is massive enough to undergo fusion of deutrium, and lithium. However, they are not massive enough to fuse hydrogen. Since deutrium and lithium are not very common, they have a limited supply of energy, and while they do produce heat, it is not enough to emit much radiation as visible light. After the slow process of fusing their deutrium and lithium is completed, they gradually cool down, becoming indistinguishable from massive gas planets. Brown dwarfs are also fairly similar in linear dimensions, slightly larger than Jupiter. Increasing the mass increases their density, without increasing their radius.
Brown dwarfs, like their smaller and larger counterparts, can exist in a variety of systems. They can orbit larger stars, orbit each other, and have smaller planets orbiting them. There may be many brown dwarfs in the universe, although they are hard to detect. They are mostly detected through their gravitational effects on stars they orbit, or through infrared astronomy. The existence of brown dwarfs is one of the many pieces of astronomical knowledge that has been discovered over the past few decades, and has enriched the subject of star and stellar system formation. Many more discoveries about how brown dwarfs form, and how they fit in with stellar systems, are being made every day.