Read this in wikipedia: "when a cell s telomeres shorten to critical lengths, the cell senesces" is that how we age?

One theory: This one biomarker of aging. Other theories include oxidative stress, and other environmental stressors, genetics, etc. Nature(genetic longevity) and nurture(environmental, how we treat ourselves, medical care) all contribute to the longevity of the human race.

Basically no: This is simplistic and doesn't fit the facts, though it may be taught as "fact" in some classrooms. The cells that bear the brunt of aging (neurons, fibroblasts) almost never divide. Mice age but don't have telomere shortening. It may be a factor in some of our cell populations (i suspect in epidermis) but it's not the magic secret any more than free radicals were a while back.