According to Wikipedia, "In human cells, both normal metabolic activities and environmental factors such as radiation can cause DNA damage, resulting in as many as 1 million individual molecular lesions per cell per day."

There are mechanisms to repair this damage, but they don't always work. Sometimes the result is cancer.

Your DNA is like a datacenter with a billion nodes that all start out with the same content in DRAM. Although error correction can compensate for most bit flips, at this scale you still get a really low mean time between failures, leading to differing memory contents over time.

An excerpt from my genetics professor:

"Even in the absence of mutagens, an average gene will mutate about once in a million generations. ~10^16 cell divisions occur in a typical life span so somewhere in cells that are part of you each of your genes has mutated 10^10 times (hence cancer)."