A nominative absolute is a free-standing (absolute) part of a sentence that describes or modifies the main subject and verb. It is usually at the beginning or end of the sentence, although it can also appear in the middle. Its parallel is the ablative absolute in Latin.

A way to remember or determine what constitutes a nominative absolute is to add a verb. You can always create a sentence out of a nominative absolute with one verb.

Their manes flowing, the horses ran from the burning barn.

Nominative absolute: "Their manes flowing."

Add a verb: "Their manes were flowing."

Stephen, his mind taxed, searched frantically for a dictionary.

Nominative absolute: "his mind taxed"

Add a verb: "His mind was taxed."

Similarly, one can break the absolute off, add a verb and make two sentences. ("Stephen searched frantically for a dictionary. His mind was taxed.")