A telomer is a region of repetitive DNA at the end of a chromosome which protects this area from deterioration. Chromosomes frequently deteriorate with age and telomers prevent this deterioration. If telomers becomes shorter as the cell ages, they can’t protect the chromosome as well.
As far as I can find, there has only been one study done measuring the length of telomers and correlating it with vitamin D levels. In the American Journal of Clinical Nutrition of November, 2007, the authors measured the length of telomers of white blood cells in women. Serum vitamin D concentration was positively associated with white blood cell telomer length.
Telomer length has been shown in other studies to be correlated with a lessened incidence of various cancers and increased cardiovascular health. And still other studies have shown increased longevity associated with higher vitamin D levels.