Looking older is entirely different than being old, although the two often happen in unison. The wrinkly look is programmed in our genes and can be vastly accelerated with an unhealthy lifestyle. It is true that we are only as old as we feel.
It is not the years that count in your life, it's the life in your years.
Biological aging is all down to your telomeres. These are found at the end of your chromosomes. On cell division a portion is lost and like a cat with 9 lives the cell can only reproduce so many times. It is natures way of ensuring we only live for a set period of time.
On the DNA level, the telomere is a dull stretch of road. It is a length of DNA monotonously made up of a recurring motif of 6 nucleotide bases (namely, the sequence TTAGGG) together with various associated proteins. The TTAGGG motif is tandemly repeated. It reads TTAGGGTTAGGGTTAGGGTTAGGGTTAGGG and so on
On average after a cell has divided between 60 and 100 times and the telomeres have been used up the cell dies. Injury to the cell causes regeneration to occur.