whats participial phrase

A participial phrase is a group of words that begins with a participle (a verb form that acts as an adjective) and functions as an adjective in a sentence. It describes or provides additional information about a noun or pronoun in a sentence.

For example:
- "The girl, holding a bouquet of flowers, smiled." In this sentence, "holding a bouquet of flowers" is the participial phrase which describes the girl.
- "The broken window was left unrepaired." Here, "broken" is the participle, and "unrepaired" is the participial phrase that describes the window.
- "He saw a dog chasing its tail." "Chasing its tail" is the participial phrase modifying the noun "dog."

is waving her arms one

Yes, "waving her arms" is an example of a participial phrase. The participle "waving" describes the action performed by the subject (she), and "her arms" provides additional information about how she is waving.