A Participial Phrase is a phrase that appears to be a verb while functions as an adjective. Noun in the sentence is modified. It can provide added description about what it is doing or what the noun looks like. These kind of sentences always start with a participial which can either be present or past participle.
In the sentence 'The broken vase, purchased by my grandmother, was suddenly falling to the floor, smashing into pieces.' The phrase highlighted fulfills the definition provided above and it is the participial phrase in the sentence.
