ablative absolute

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun In Latin grammar, an adverbial phrase syntactically independent from the rest of the sentence and containing a noun or pronoun plus an adjunct, usually a participle or adjective, with both elements in the ablative case.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun linguistics A construction in Latin in which an independent phrase with a noun in the ablative case has a participle, expressed or implied, which agrees with it in gender, number and case – both words forming a clause grammatically unconnected with the rest of the sentence.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a constituent in Latin grammar; a noun and its modifier can function as a sentence modifier