ablative absolute

American Heritage® Dictionary of the English Language, Fourth Edition

1. n. 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.

Wiktionary

1. n. 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.
2. n. 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.

GNU Webster's 1913

1. a construction in Latin, in which a noun in the ablative case has a participle (either expressed or implied), agreeing with it in gender, number, and case, both words forming a clause by themselves and being unconnected, grammatically, with the rest of the sentence; as, Tarquinio regnante, Pythagoras venit, i. e., Tarquinius reigning, Pythagoras came.

WordNet 3.0

1. n. a constituent in Latin grammar; a noun and its modifier can function as a sentence modifier