Jean Grey answers this question in the first X-Men movie:
Dr. Jean Grey: "His mutation. He has uncharted regenerative capabilities, enabling him to heal rapidly. It also makes his age impossible to determine. He could very well be older than you, Professor."
Now for the biology of the aging process itself... it's divided up into two factors. There are programmed factors, which is essentially things like growth, life stages, and development, dependent on species. Then there's damage related factors like environment or unstable genes. We as humans mature and reach peaks in our 20s. Any additional years tacked on afterwards is just a fully matured organism decaying.
Now let's go to 1800s before our medical advances of today. Average human life span was 38.8 yrs old, yet people didn't mature physically any slower or faster. It was still humans reaching physical peaks and being fully physically matured in the 20s, no sooner or later, but since we didn't have the advances in medicines that we did, serious diseases would either kill us off, or take a physical toll on our body, AGING it so to speak. Today our average life span is in the 70s, yet we are fully physically matured in our 20s, no sooner or later. We just slowed the damage-related factors by a lot to extend our years past our biological peak.
Now take Wolverine who is essentially still a human, and would go through same growth periods and life stages. When they say he has slowed aging, they don't mean his cells actually physically produce and grow at slower rates. They say he has slowed aging because he doesn't have to worry about damage-related factors. Whenever any damage is done, it's instantly healed up, and his body doesn't have to go through damage-related stress aging. It's equivalent to our medical advances increasing our life spans, and a 40 year old today compared to a 40 year old from the 1800s would be perceived as having aged slower because of that.