A participial phrase consists of a participle and any modifiers or complements the participle has. The entire phrase is used as an adjective.
Examples: Reaching for a bagel, she knocked over her glass of milk. [The participial phrase modifies the pronoun she.]
Aunt Molly sent me a baseball glove autographed by Sammy Sosa. [The participial phrase modifies the noun glove.]
A participial phrase should be placed as close as possible to the word it modifies. Otherwise, the phrase may appear to modify another word, and the sentence may not make sense.
misplaced: Many holiday decorations adorned the gift shop made of papier mache.
corrected: Many holiday decoration made of papier mache adorned the gift shop.