Writing about one's experiences allows one to relive experiences and allows others to relive the experience when they read it. Writing expresses thoughts that would have otherwise been memorized. When we have a persistent thought pattern and do not write it down the mind continues to go over those thoughts in an effort to not lose them but when you write them down you no longer need to go over those ideas. The writing acts like an external memory extending our capacities for thinking.
Writing offers a mechanism for reinforcing memories and solidifying them. It also allows one to process experiences to better understand them. Through writing one can take different perspectives. It offers a glimpse into more of the world then one could have realized without writing it down or otherwise committing it to memory.
Writing can offer a means of trimming memories in that when one writes one creates a sequence that omits certain pieces of information. This allows the overall story to be told without having to remember all of the details. Unfortunately, important details can get lost in this process as well.
The more one writes the more one creates pathways that reinforce the consolidation of experiences into words and narratives. This process helps the mind process daily life in a way that supports and reinforces linguistic specificity.
Communicating via narrative is the main way humans pass on knowledge and therefore any activity that solidifies lessons will be selected for and valued. Prior to widespread formal written language lessons were passed down via oral traditions but writing allows for messages to be shared in a more permanent and spreadable way. One person with a good story was no longer limited to sharing their message with those in their immediate environment. With writing and now the internet messages are spread throughout the world.