The baritone guitar is a longer-scale six-string instrument that is usually tuned B to B (B E A D F# B) or A to A (A D G C E A) and sits between the ranges of the standard guitar and the four-string bass. There many types of baritones, including electric, acoustic, and 7 and 8-strings, and the instrument has maintained a distinct position on the outer edge of the guitar community for decades. It is found in many styles of playing from country to heavy metal.
The first baritones were used to play classical music but it was Danelectro that made the original electric baritone guitars near the end of the 1950s.
Danelectro 56 Baritone Reissue Electric Guitar
The electric baritone quickly found a home with the surf/instrumental bands of the period, in film soundtracks, and in country music, where it was muted, called "tic tac bass" and employed to double the part of the actual bass player. In the modern era, baritones have become common in metal and some types of jazz and improvised music. 
Country Baritone Lesson
Metal Baritone Demo.
There's no standardized tuning for baritone guitar but the most common are a Perfect Fourth below a standard guitar (B E A D F# B) and a Perfect Fifth below (A D G C E A). Both tunings also get the Drop D treatment applied to them, lowering the bottom string an additional Whole Step, especially in rock and metal playing. Scale length for electrics can vary from 25.5" to 28.7" and an average set of baritone strings is gauged from .012" to .054". Shorter-scale baritones are normally tuned to B, while longer-scale models can go from A to A without losing string tension. Acoustic baritones can feature scale lengths up to 30.5".
Baritone guitar history can be traced back to the viola da gamba of the 1400s, a fretted cello-like instrument with anywhere from five to seven strings and the first mandocellos produced by Gibson beginning in 1905. German luthiers of the 19th Century also built baritone guitars while experimenting with the voices of instruments of varying size. What we think of as a baritone guitar is a pretty modern instrument, beginning with Danelectro's six-string basses and baritones of the mid-20th Century. It was first used in heavy metal during the late 1980s by bands like Bolt Thrower and Carcass when lowered tunings first began to become popular.
Early baritone users include Duane Eddy, who employed the Danelectro baritone on many of his instrumental hits. Beach Boy Brian Wilson also found regular use for baritone guitars in his arrangements. Crossover country artist Glen Campbell played baritone guitar on his hits "Wichita Lineman" and "Galveston." Joe Perry of Aerosmith also used a baritone on "Back In The Saddle" in 1976.
Baritone guitars have become much more common in the modern day and have been used by a wide variety of rock, metal, and jazz players. Dave Matthews, Robert Smith of The Cure, Mike Mushok of Staind, and Pete Loeffler of Chevelle are all baritone users, as is Pat Smear of Foo Fighters. Baritone players in the metal community include Pat O'Brien of Cannibal Corpse, Dino Cazeres of Fear Factory, James Hetfield of Metallica, and Stephan Carpenter of Deftones. Pat Metheny is the best-known baritone user in the jazz world, featuring them on his releases One Quiet Night and What's It All About.