http://www.answers.com/topic/natty has this definition for 'natty':

"nat·ty (năt'ē)
adj., -ti·er, -ti·est.
Neat, trim, and smart; dapper.

[Perhaps variant of obsolete netty, from net, elegant, from Middle English, from Old French. See neat1.]

nattily nat'ti·ly adv.
nattiness nat'ti·ness n.

The adjective natty has one meaning:

Meaning #1: marked by smartness in dress and manners
Synonyms: dapper, dashing, jaunty, raffish, rakish, smart, spiffy, snappy, spruce"

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http://takeourword.com/TOW127/page2.html provides this information about the origin and meaning of the word 'natty':

"Most etymologists seem to favor the explanation that the word is a variation of the obsolete netty "neat, elegant" from Middle English net "clean, tidy" (14th century). This would make it a relative of modern English neat, which also comes from Middle English net. Net also meant "neat, clean" in Old French, hence modern French nettoyer, "to clean". The source of the Old French word is Latin nitidus "elegant, shiny", from the verb nitere "shine".   

Interestingly, neat dates from the 16th century, while natty first appears in the 18th century in Grose's Dictionary of the Vulgar Tongue: "Natty lads, young thieves or pickpockets." The Indo-European root here is *nei- "to shine", which may have given English the word lilac, from Persian nil "indigo"."