Telomeres are ends of chromosomes that shorten with each time cell divides. When the telomere is completely gone, the cell does not divide any more. This is kind of like the caps at the end of a shoe lace. If the caps come off, the shoe lace comes untangled.
Now stress is found to accelerate the telomere reduction. This is because telomerase an enzyme that protects telomeres and also promotes telomere repair seems to be reduced in people under stress.
This also explains how severe stress cause bags under eyes and wrinkles faster.
The connection between mind and telomerase production is not clear though.