Answer:
A gerund is a form of a verb used as a noun, whereas a participle is a form of verb used as an adjective or as a verb in conjunction with an auxiliary verb. An appositive is a noun or noun phrase that modifies a noun. This grammatical construction usually sits next to another noun and modifies it by renaming it or describing it in another way. Appositives are generally offset with commas or dashes.
Examples:
Gerund: Verb: Read; Gerund: Reading; Sentence: Her favorite hobby is reading.
Participle: A participle is an adjective made from a verb. Verb: Sleep; Participle: Sleeping; Phrase: The sleeping dog.
Appositive: Sentence: "The boy raced ahead to the finish line"; Appositive: "The boy, an avid sprinter, raced ahead to the finish line."
For the first two, the difference is really the context of the phrase/sentence. The gerund turns the verb into a noun, turning the <em>action </em>of reading into a <em>thing, </em>or a <em>hobby</em>. A participle phrase takes the <em>action </em>of sleeping and turns it into an adjective, and results in "the sleeping dog."