What is Winston speaking of when he says, "I understand HOW: I do not understand WHY" in Part One, Chapter Seven, of George Orwell's 1984?
This quote refers to Winston's role in rewriting Oceania's history. He understands how this is carried out: the Party uses the Ministry of Truth to destroy information and disseminate its own creations. In this case, the Party labelled several of its members as enemies of state after they allegedly conspired with the Party's enemy, Eurasia. The Party then used Winston and others at the Ministry of Truth to destroy all of the information which suggested otherwise.
But, as Winston comments, he knows that there is a deeper meaning to the Party's falsification of the past:
The ultimate motive was mysterious.
This burning question ("I do not understand WHY") foreshadows an important event in Part Two of the story when Winston receives "the book" from O'Brien. In this book, Goldstein offers an explanation to Winston's question. He argues that war, whether the enemy is Eurasia or Eastasia, is a necessary tool in maintaining the Party's supremacy and total control. Through war, the Party can legitimise its unequal distribution of wealth, by telling the people that it needs Oceania's resources as part of the war effort. This keeps the people in a state of poverty and need: they will accept the Party and its rules because they desire protection and prosperity.
Thus, by asking this question, Winston not only embraces the spirit of rebellion but also sets the scene for the key moment when he receives Goldstein's book.
In order to get the answer to this, just look above the line that you quote to us. If you look there, you will see that Winston is referring to his job. He is talking about how the Party takes the past and changes it. Here is the quote you are looking for:
The immediate advantages of falsifying the past were obvious, but the ultimate motive was mysterious. He took up his pen again and wrote:
I understand HOW: I do not understand WHY.
Winston wonders this when he finds the picture of those three guys in a situation that totally makes a lie out of the Party's official history. He wonders why the Party would go to such lengths (paying him and so many others like him) to tell lies about the past.