Meaning: This sentence describes the elegant movement of leaves on swaying branches. It's like saying,
Choice of Words: "Leaves" is the subject of the sentence. "Dance" is a verb that describes the movement of the leaves. "Graceful" describes the beauty of the leaves' movement. "On" describes the position of the leaves. "Branches" is the object that the leaves are dancing on. "Sway" is a verb that describes the movement of the branches.