The Collaborative International Dictionary of English v.0.48:

Bayou \Bay"ou\, n.; pl. Bayous. [North Am. Indian bayuk, in F.
   spelling bayouc, bayouque.]
   An inlet from the Gulf of Mexico, from a lake, or from a
   large river, sometimes sluggish, sometimes without
   perceptible movement except from tide and wind. [Southern U.
   S.]
   [1913 Webster]

         A dark slender thread of a bayou moves loiteringly
         northeastward into a swamp of huge cypresses. --G. W.
                                                  Cable.
   [1913 Webster]

WordNet (r) 3.0 (2006):

bayou
    n 1: a swampy arm or slow-moving outlet of a lake (term used
         mainly in Mississippi and Louisiana)