A participial phrase is comprised of a participle and its modifiers, objects and complements. The entire phrase often serves as an adjective. Participial phrases can appear anywhere in a sentence but must always be placed as near to the noun they modify as possible.
Definition of a Participle
A participle is a verb form. A present participle ends in -ing. A past participle usually ends in -ed. Participles look like verbs, but they function as adjectives. Adjectives answer the questions "what kind, which one, how many, how much" for a particular noun or pronoun. For example, "A singing bird can create joy in the heart." "Singing" is not a verb describing what the bird is doing; it is a participle describing what kind of bird it is.
Take a participle and add on some modifiers, objects and complements and it becomes a participial phrase: "Singing softly in its nest at dawn, the bird brought joy to my heart." The participle is still "singing" and it still modifies "bird," but now it has been expanded. What kind of bird is this? A "singing softly in its nest at dawn" kind of bird.
Placement of Participial Phrases
Very often participial phrases appear the beginning of a sentence, but they can appear anywhere else. In the previous example, the participial phrase can be moved to the middle of the sentence:
The bird, singing softly in its nest at dawn, brought joy to my heart.
A participial phrase may appear at the end of the sentence as well:
I heard the bird singing softly in its nest at dawn.