You know that the title of the book is The Golden Compass, but let's not forget that it's also the first book in the series called His Dark Materials.
The Golden Compass
The golden compass, also known as an "alethiometer," is a gadget given to Lyra by the Master of Jordan College at Oxford. The device is powered by Dust and can be used to gain insight into any number of questions. As Farder Coram tells us in Chapter 7, "aletheia" is Greek for "truth," so "alethiometer" means "truth measure" (7.118). It's a bit ironic that the designated keeper of this particular alethiometer is Lyra, who is known for telling whoppers.
Why title the book The Golden Compass? Maybe it's because Lyra's growing skill with this instrument of the divine proves to the reader that there's something very special about her – and it allows her to harness a power of her own.
The titles of the other two books in the trilogy also feature objects: The Subtle Knife and The Amber Spyglass.
P.S. The original title for this book is Northern Lights. Actually, it's only published as The Golden Compass in North America. The original title shifts the focus away from the alethiometer and toward the scene under the northern lights where Lord Asriel creates a bridge to another world. Which title do you like better?
His Dark Materials
The phrase "His Dark Materials" is a line from Book II of Milton's Paradise Lost, which you can read all about on Shmoop. For more on the phrase "His Dark Materials," zip over to our section on the novel's epigraph, which contains the phrase.
In The Golden Compass, those "Dark Materials" presumably refer to Dust, which – as Lord Asriel tells us in Chapter 21 – the Church interprets as evidence of original sin. For more on that topic, head over to "Symbolism, Imagery, Allegory: Dust (and Original Sin)."