Telomeres shorten anytime a cell divides. As cell generations get older and older, the telomeres get shorter and shorter. With each shortening they are less likely to divide. It's a reason why an 80 year old heals slower than a 20 year old. It's also a theory as to why we age though there are several several other factors at play such as...
1-when we get older, more DNA errors accumulate
2-our vasculature feeds our body with nutrients and energy, as we get older, our vasculature can't do this as well due to arterio and atherosclerosis
3-our organs on a macro-level accumulate structural weaknesses that cannot be healed, e.g our heart calcifies with each heart beat, which is why the theory goes if you do cardio, your baseline heart rate slows down, helping you to live longer.
4-Several enzymes produced by the body are not done so as well when we get older, several of which likely have strong beneficial properties such as superoxide dismutase, an antioxidant powerhouse
5-Several components of our body, once lost, aren't replaceable or very difficult to replace such as scar tissue, loss of cardiac tissue, neurons, etc
6-our body starts to produce by-products it can't get rid of that aren't beneficial such as amyloid plaques
There's more but you get the point.
A theory with telomeres is that they shorten, thus reducing a cell's ability to divide, because it's actually protective as we get older though we will not heal as fast. The theory goes that with each cell division, more and more genetic errors accumulate because the DNA replication process is not 100% accurate. The more the cell divides, the more likely there will be cancerous cells produced.
Which is why if Wolverine really existed, he'd likely get cancer. Only way to prevent that is a super-immune system, but the more active an immune system is, the more likely it is to attack it's own body--thus cancelling out the likelihood of a real Wolverine, that and that cells reproducing would require tons of nutrients (imagine him having to eat almost non-stop to heal the way he does), and would normally take weeks on the order that he does it.
