As cells replicate, their DNA gets shortened. The DNA has extra non-coding DNA at the ends that get clipped off when it replicates  (this extra DNA acts as a sort of a buffer at the ends of the chromosomes, so the important coding part of the DNA does not get clipped off). It is the job of an enzyme called telomerase to add on the extra non-coding DNA after each replication. Telomerase allows the cell to replicate its DNA, but still with each replication the chromosomes get shorter.

With time cell replication can only go on for so long, due to so much trimming off of the ends of the chromosomes. It has been found that in about 75% of spontaneous melanomas and many familial melanomas that there is a mutation that allows the telomerase to be hyperactive (adding on lots of non- coding DNA buffer to the ends of the chromosomes) thereby allowing the cells to replicate and replicate without end. The exciting news is that this knowledge will lead to new therapies for melanoma aimed at taming the telomerase enzyme.
Julie E. Voss, M.D.

http://www.dkfz.de/en/presse/pressemitteilungen/2013/dkfz-pm-13-06-Gene-Mutation-Immortalizes-Malignant-Melanoma.php