The Time-Turner only appears at the very end of the novel, though we see its effects throughout in Hermione's stress and odd appearances and disappearances, her heavy course load, and her weird conversation with McGonagall at the start of the year. The Time-Turner basically becomes the star of the final chapters of the book; the entire plot hinges around it.
So what does it represent in the novel? Oddly enough, it represents limitation as much as it does possibility. The Time-Turner seems like a super power, like something someone on Heroes would own – and who wouldn't want their own personal time travel machine? But, as Hermione reveals, it comes with a lot of rules (21.112). And even when Hermione and Harry break those rules and go back in time to save Sirius, they can only do so much. Time and Time-Turners are dangerous, and Hermione knows (and Harry learns) not to mess around with it.
In a way, playing with time is too much like playing god, which is pretty much the problem with the power-hungry Voldemort in a nutshell. It's no mistake that Hermione returns her Time-Turner at the end of the year – the stress of using it and the danger it poses are a bit too much for her.