An absolute phrase is a noun phrase which modifies a sentence.  It adds more information to the sentence.  An absolute phrase refers to the group of words that accompanies an independent phrase. This group of words consists of a participle and a noun. It is not necessary to the sentence which stands on its own, but it adds more information. It does not contain a finite verb, it can come at the beginning or the middle or the end of a sentence, and

examples of absolute phrase usage

God willing, we will arrive safely.
God willing is the absolute phrase.
The waves building, we decided not to do into the ocean.
Left to fend for themselves, the children decided to build a fire.
We will set out at dawn, weather permitting.

There are two kinds of absolute phrase:

The first refers to those demonstrated by the above sentences are adding a cause of or a condition related to the rest of the sentence. They can be interchanged with a subordinate clause beginning with the words if, since, because, as, after or when. For example:
We will set out at dawn if the weather permits.

The other type of absolute phrase could be introduced with the proposition with or being, and could also operate as a main clause.  In other words this type of absolute phrase combines two clauses with different subjects (and could be two separate sentences.)
The noise died down. We fell asleep.
We fell asleep, the noise having died down.

An absolute phrase is a noun phrase which modifies a sentence.  It adds more information to the sentence.