Recently I've been reading Robert Cialdini's "Influence: the psychology of persuasion". In his book, the psychologist explains how car salesmen, cops and Tupperware salespeople employ persuasion techniques in order to encourage costumers to buy cars, thugs to confess their crimes and transform your friends into salesmen. I believe one of the many examples contained in the book can explain why writing stuff down is such an effective practice.
It has to do with American prisoners of war in Chinese camps during the Korea war.
Cialdini explains in his book that in an attempt to change the prisoners' minds about communism, Chinese officials in charge of prisoner camps would encourage the American captives to write essays about their views on politics and war. Often, a little prize was given to the prisoner who wrote the best essay. The Chinese did not force the prisoners to write favourable statements about China or communism, however it was clear that the winning essay often had an understanding attitude towards anti-capitalists politics. At the end of the day, prisoners knew that by writing somewhat positive words towards the enemy they could get a prize. It is important to note that no radical changes in one's beliefs was required, just you had to make mild concessions to the Communist lifestyle in your essay to get a chance to win the prize.
In fact, it's not some kind of Pavlovian conditioning the Chinese were after. The prisoners' opinions certainly would have not changed, had the Chinese tried to train them with rewards like you do with dogs. It was not the "nice words about communists = more food" equation they were after, but it was something deeper.
The effect the Chinese were seeking was that of commitment. Once you write some words, you commit to what you write. You feel the need to stand behind those words you put on paper. It's both a social and internal effect: when we commit to something, when we state publicly that we will do something, we feel pushed to accomplish that goal both by peer pressure and by something inside of us that tells us we should be coherent with ourselves. Words that are blatantly incoherent with our personal views of course don't count, but the mild concessions to views different from ours can really get us to behave differently.
As an aside, this commitment behavior is the reason why people who are trying to quit smoking should tell as many people as they can of their intentions: they will feel pressured to follow their public commitment and thus will be more likely to really stop smoking.
So, the takeaway here is that by writing down stuff we feel compelled to remain true to our words. What's more, it's not even necessary that other people know of our commitment for this mechanic to work.