The group of words that improves an independent clause is called an absolute phrase. It is composed of a noun and its modifiers which often include a participial phrase ending in “ing.” An independent clause, on the other hand, is a group of words that has a subject and verb giving the sentence a complete thought.
In our example sentence “The baby toddled across the room with his first wobbly steps, his chubby legs pumping.”, “The baby toddled across the room with his first wobbly steps.” Is our independent clause and “his chubby legs pumping” is the absolute phrase.