i wouldn't say there is a moral, since morals are usually those आप can apply to your life, but twilight stands for the "twilight" of your life. The point of your life where it is just beginning and आप haven't fully experienced everything just yet.
There's alot आप can relate to in Twilight, the characters to some extent, and the situations they go through, but I don't consider Twilight to have a specific moral to it. The plot? Forbidden Fruit. It is somewhat "forbidden" for a human and vampire to be together. Edward is the predator. Bella is the prey. It goes against the nature. But, they irrevocably fell in प्यार and continued to be together despite "destiny" and "fate". We discover later that it is however forbidden for a human to know the existence of vampires. The Volturi enforce the "laws" as they pose as royalty for all vampire kind. To the Volturi, Bella and Edward's relationship is forbidden, but the curiousity behind the attraction they feel for one another keeps them alive.