1 {Harry, Ron, and Hermione walking along a corridor in Hogwarts}
2 [sound]: Appear! {another copy of Hermione appears!}
3 Harry: Hermione! What are you doing... in two places at once?
3 Hermione 2: I came back with the time turner to warn you.
4 Hermione 2: A terrible destiny awaits you and that dreamy exchange student, Will!

The Time Turner appears in Harry Potter and the Prisoner of Azkaban.

I trust that with the book now 9 years old and the film 4 years old, we're out of people being worried about spoilers on this one.

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2020-01-19 Rerun commentary: Giving Hermione a Time-Turner was perhaps the single most irresponsible thing that Professor McGonagle did in the entire history of Hogwarts. Quoting from Harry Potter Wiki (which is about the best-researched source of canon for the Harry Potter universe):

Time-related magic is unstable, and serious breaches in the laws of time result in catastrophic events. Possible scenarios include a wizard or witch killing their past or future selves by mistake, or altering one's life path in such a drastic fashion that it can result in temporal anomalies such as un-births. [...] The consequences of meddling with time could be as severe as creating an alternate timeline, such as one in which Lord Voldemort was never defeated and still ruled.

Now, imagine giving a high school student something that could do this sort of thing, and trusting them not to mess up the universe. Okay, granted, it was Hermione... but still.