In the Twilight series, it is very well known to readers and anyone that's heard about the series that the vampires in the series "sparkle". Is a reason ever given as to why the vampires sparkle in the sunlight? If so, why?
Stephenie Meyer often mentions that vampires from the Twilight series have stone-cold and marble-like skin.
I doubted his icy marble skin would smell anything like food. - New Moon
That she was a vampire was obvious. Her skin was marble white, the texture a million times smoother than human skin. Even under the clouds, she glistened ever so slightly. - Breaking Dawn
Notably, their skin is compared to marble and crystal:
Edward in the sunlight was shocking. I couldn't get used to it, though I'd been staring at him all afternoon. His skin, white despite the faint flush from yesterday's hunting trip, literally sparkled, like thousands of tiny diamonds were embedded in the surface. He lay perfectly still in the grass, his shirt open over his sculpted, incandescent chest, his scintillating arms bare. His glistening, pale lavender lids were shut, though of course he didn't sleep. A perfect statue, carved in some unknown stone, smooth like marble, glittering like crystal. - Twilight
Apparently, the in-universe explanation is that vampires' skin is similar to a precious stone that sparkles in the sunlight.
If I recall correctly I remember reading that Stephenie Meyer had a dream about vampires sparkling in the sun and she included the detail in her books. I found an FAQ on IMDB that mentions the same thing here.
In this link Stephanie Meyer herself answers that question in the "Vampires and Pregnancy" section.
'Cause it's cool .
(Sorry, that really seems to be the only reason. None other is given in the books or movies. According to popular legend Stephenie Meyer literally dreamed it up.)
 may also be considered "cute", "fun", "beautiful", "amazing", "inspiring", "dreamy", "gay" (as in happy by the writer(s) and real fans.