"small natural stream," Old English broc "flowing stream, torrent," of obscure origin, probably from Proto-Germanic *broka- which yielded words in German (Bruch) and Dutch (broek) that have a sense of "marsh, bog." In Sussex and Kent, it means "water-meadow," and in plural, "low, marshy ground."
"bifurcated garment worn by men, covering the body and waist to the knees," c. 1200, a double plural (also breechen, and singular breech), from Old English brec "breeches," plural of broc "garment for the legs and trunk," from Proto-Germanic *brokiz (source also of Old Norse brok, Dutch broek, Danish brog, Old High German bruoh, German Bruch, obsolete since 18c. except in Swiss dialect), perhaps from PIE root *bhreg- "to break." The etymological notion would be of a garment "forked" or "split." The singular breech survived into 17c., but the word is now always used in the plural.
The Proto-Germanic word is a parallel form to Celtic *bracca, source (via Gaulish) of Latin braca (source of French braies, Italian braca, Spanish braga). Some propose that the Germanic word group is borrowed from Gallo-Latin, others that the Celtic was from Germanic, but OED writes that the Proto-Germanic noun "has all the markings of an original Teutonic word."
Classical bracae were part of the characteristic garb of Gauls and Orientals; they were not worn by Greeks or Romans until the end of the republic. After 1c. they came into use at first among military forces stationed in cold climates and were adopted generally toward the end of the empire, though they never seem to have been much in favor in Rome proper.
The expanded sense of "lower part of the body, part of the body covered by breeches, posterior" led to senses in childbirthing (1670s) and gunnery ("the part of a firearm behind the bore," 1570s). As the popular word for "trousers" in English, it was displaced in U.S. c. 1840 by pants. The Breeches Bible (Geneva Bible of 1560) is so called on account of rendition of Genesis iii.7 (already in Wycliffe) "They sewed figge leaues together, and made themselues breeches."