Why are reveries sometimes called "brown" studies?
From TheFreeDictionary.com:
brown study n a mood of deep absorption or thoughtfulness; reverie ...
Gloomy meditation or melancholy is known as being in a brown study.
This is a somewhat archaic usage (it may be a rural or Southern U.S. regionalism, but I don't have access to my tools for tracking that down just at the moment), although it has been used in poetry to good effect. Consider this stanza from John Crowe Ransom's "Bells for John Whiteside's Daughter":
There was such speed in her little body,
And such lightness in her footfall,
It is no wonder her brown study astonishes us all
He's talking about death as a "brown study" in an example of understatement.
Edit
@Kit brings up a good point. "Brown" used to mean gloomy exclusively. From Etymonline:
brown O.E. brun "dark, dusky," only developing a definite color sense 13c
Slightly surprisingly, since neither of its words now seems to fit the meaning, brown study was originally a tautology and pleonasm.
The OED first cites it from 1552*. As other answers note, brown at this date could mean dusky, dark more generally than today, and hence figuratively gloomy, serious. But besides that, study also had a slew of now-obsolete meanings, including a state of mental perplexity or anxious thought and a state of reverie or abstraction, with uses like:
He was in suche a study he herd not what Gouernayle said.
—Malory, Morte d'Arthur, 1470–85
I was at first in a study what to do, at last I promised.
—R. Meeke, Diary, 1689
So a brown study then was closely analogous to the not-yet-so-opaque a blue funk. To be in a study was bad already; a brown study really served to emphasise the gloom.
* in the rather extraordinary-sounding Manifest Detection Diceplay, which turns out upon googling to be a pamphlet on cheating at cards, A Manifest Detection of the Most Vyle and Detestable Form of Diceplay, by one Gilbert White.
According to the Phrase Finder, brown study is very old usage of "brown" to indicate a gloomy mood and "study" in the sense of deep thought. More modernly, we would probably more immediately grasp "black mood," since black is the new brown, as it were.
The closest meaning today of 'brown study' is 'brooding'. As used into the mid-20th century, didn't just mean a melancholy mood or 'reverie' and it didn't mean 'depressed' in our usual sense. It meant thinking so deeply about something troubling that one becomes wrapped up in it and temporarily cut off from other people or asocial. In essence, if one is in a brown study, one is 'studying' (thinking hard about) something in a 'brown' or darkly shadowed mood.The assumption was, though, that people going into brown studies occasionally and then come out of them.
Charles Mackay, A Glossary of Obscure Words and Phrases in the Writings of Shakspeare and His Contemporaries (1887) has an interesting but rather lengthy entry for "Brown study," parts of which I reproduce (with annotations) below:
Brown study. Many conjectures have been hazarded as to the origin of what [Robert] Nares [in A Glossary: Or, Collection of Words, Phrases, Names, and Allusions to Customs, Proverbs, &c. (1822)] calls "this singular phrase." It means, to be deep in serious meditation.
...
"Brown-deep" according to Mr. [James] Halliwell [in A Dictionary of Archaic and Provincial Words: Obsolete Phrases, Proverbs, and Ancient Customs (1855)] and Mr. Thomas Wright [in Dictionary of Obsolete and Provincial English (1857)], is a local phrase in Kent and Wiltshire, applied to one lost in reflection. [James Hotten,] The Slang Dictionary (1874) defines a brown study as a reverie, and adds, "Very common even in educated society, but hardly admissible in writing, and therefore considered a vulgarism. It is derived by a writer in 'Notes and Queries [April 27, 1850],' from brow-study! the old German braun or aug-braun, an eyebrow!"
The derivation of brown study is wholly unconnected with colour, and is from the Keltic brou, melancholy, sadness, grief, mourning; whence a "brown" study is a sad or melancholy reverie or study; "brown-deep," deep in sadness, whence the Gaelic., bronach, sad mournful; bronag, a sorrowful woman; bron-bhrat, a pall over a coffin, a mort-cloth, a mourning hat-band, &c.; and broin, lamentation, sorrow.
The Notes and Queries suggestion is less impressive than it might at first seem. A correspondent identified as "D. V. S." had posted this item in the March 30, 1850, issue of Notes and Queries:
"Brown Study"—a term generally applied to intense reverie. Why "brown" rather than blue or yellow? Brown must be a corruption of some word. Query of "barren," in the sense of fruitless or useless?
That query drew this response from "Hermes" in the April 27, 1850, issue of the same periodical:
Brown Study (No. 22. p. 352.).—Surely a corruption of brow-study, brow being derived from the old German, braun, in its compound form ang-braun, an eyebrow. (Vide Wachter, Gloss. Germ.)
With all due respect to the confidence with which "Hermes" introduces it, this submission reads like a free-association response offered as an answer on EL&U. And don't call me Shirley!
Meanwhile, Mackay's derivation of "brown" in the sense of "melancholic" from Keltic doesn't seem to have gained much traction over the years. Ernest Weekley, An Etymological Dictionary of Modern English (1921), for example, has this:
With brown study, "gloomy meditations" ([Samuel] Johns[on]), we may perh[aps] compare F[rench] offusquer, to overshadow, create melancholy absorption, from L[atin] fuscus, brown.
George Apperson, English Proverbs and Proverbial Phrases: A Historical Dictionary (1929) introduces the interesting fact that brown was a latecomer to the original expression:
Brown study, To be in a. Originally simply 'in a study', and this form persisted for centuries after the inexplicable 'brown' had been introduced, (a) In a study, simply, c. 1300: Robert of Brunne, tr. Langtoft's Chron., 58 (Hearne), Whan Edward perceyued, his herte was in studie. c.1386: Chaucer, Knight's Tale, l. 672, Into a studie he fil sodeynly. 1485: Malory, Morte d'Arthur, bk i ch 20, The kyng sat in a study. 1576: Pettie, Petite Pallace i 72 (1908), This youth stood staring in her face in a great study. ...
Julia Cresswell, Oxford Dictionary of Word Origins, second edition (2009) finds the relevant sense of brown lurking in the English word brown all along:
brown {OE} In Old English brown simply meant 'dark'. It acquired its modern sense in Middle English. The idea of darkness developed into a further sense of 'gloomy or serious', and this is the sense that occurs in the 16th-century phrase a brown study, 'absorbed in one's thoughts'. The use of 'study' is puzzling to us today. It is not a room for working in, but a state of daydreaming or meditation, a meaning long out of use in English.