("Playing with her jump rope" describes the girl.)
Participial Phrase - I watched the little girl playing with her jump rope.("Hopping through the forest" is a noun - the direct object of the verb "loved.") Gerund Phrase - The rabbit loved hopping through the forest.("Hopping through the forest" describes the rabbit.)
Participial Phrase - Hopping through the forest, the rabbit noticed a new watering hole.But in gerund phrases, the phrase that starts with an -ing verb functions as a noun, not as an adjective. Gerund phrases are another type of verbal phrase that uses -ing verbs. "The dog crashed into the wall" is a grammatically correct sentence, but it helps the reader to know that the dog was running at a high speed. However, they do add important information that gives the reader a better idea of what is happening.
That means the sentence still makes sense if you remove the participial phrases. When participial phrases are separated from the sentence by a comma, they are non-essential. Jack watched the giant, sleeping soundly, as he crept by.The baby, crying loudly and continuously, kept her parents up all night.Running at high speed, the dog crashed into the wall.When you add words to these participles, you're making participial phrases. However, they are not functioning as verbs in these sentences they are functioning as adjectives. Running, crying and sleeping are all verbs. Jack watched the sleeping giant as he crept by.The crying baby kept her parents up all night.Participles provide further information about the noun or nouns in a sentence, just like an adjective or adverb. A participle is a verb that functions as a modifier.