What is the significance of the titles for Twilight, New Moon and Eclipse?
All four titles relate to the moon and the changing parts of the day. Twilight is the time of day right before sunset, when the last light of day gives way to night. Edward tells Bella that twilight is the hard part of the day for him, because it's the time when darkness comes, and it reminds him of his lifetime of endless night/darkness as a vampire. Later in the book, he also talks about how Bella wants that to be the "twilight of her life," because she wants him to end her human life and turn her into a vampire. But he isn't ready to end her life when it has barely just started.
The new moon is when the moon goes dark; it's the time of the lunar cycle when the moon is closest to the sun. In this book, the "new moon" refers to the darkness Bella feels when Edward leaves, as well as the transformation of Jacob Black into a wolf. The link between wolves and moons is fairly common, and since this is a new life for Jacob, it links well to the title.
Eclipse is what happens when the sun and moon line up together. One eclipses the other, blocking it out from sight to the people on earth. There is a quote about this in that book, but I can't find it right now, unfortunately. In general, you can think of the idea that in this book Bella feels very torn between Jacob (her sun) and Edward (her moon). One will have to "eclipse" the other for her eventually, when she decides between them.
These are all just my own interpretations; I'm sure other people's ideas will vary.
I think all three titles stand for phases in Bella's life as well as playing on the fact that fact that these phases make the world dark which is the best time for vampires to evade the human world. Twilight would stand for the beginning and the end of Bella's world. Twilight brings beautiful light which would be Edward and then darkness soon follows after twilight which would being dragged into the dangerous world of that is Edward's. New Moon would signify Bella's time of darkness since a new moon is there is no moon to shine at all which would be Edward. Eclipse would be the happiness that is shortly shadowed by Edwards dark world.
In Twilight edward says that twilight is the safest time for vampires,In New Moon Bella felt like her life was like a new moon cause it was so dark without Edward. You know like how you cant see a new moon. Eclipse im not sure about but it probably says somethin bout a eclipse in it