The Architect explains later in the conversation:
The Architect: [The Oracle] stumbled upon a solution whereby nearly 99% of all test subjects accepted the program, as long as they were given a choice, even if they were only aware of the choice at a near unconscious level. While this answer functioned, it was obviously fundamentally flawed, thus creating the otherwise contradictory systemic anomaly, that if left unchecked might threaten the system itself. Ergo those that refused the program, while a minority, if unchecked, would constitute an escalating probablility of disaster.
Neo: This is about Zion.
During this conversation the both Neo and Architect specifically say that "the problem is choice".
The problem with choice is that some humans in the Matrix choose to reject it, causing anomalies (errors) in the system which eventually add up to destabilize the entire system. The One is the integral anomaly -- the sum of all those anomalies/errors. The One solves the problem by summing up (integrating) all those individual anomalies and returning to the Source to cancel them out. As explained by the Architect:
The function of the One is now to return to the Source, allowing a temporary dissemination of the code you carry, reinserting the prime program.
Essentially, the One deletes himself by returning to the Source (recall that's how programs are deleted as well), removing all those anomalies and restabilizing the system. This also causes a reboot of the entire Matrix, starting the next cycle.
As the One meets with the Architect to make his final choice (to return to the Source or not), the Machines simultaneously destroy Zion. This eliminates all the people who rejected the Matrix, and ensures that the One returns to the Source by blackmailing the One with the threat of the extinction of the human race (since Zion will be destroyed, and the Matrix will crash and kill everyone in it).
Although the problem is choice, it results in a more stable system than the system of coercion (even blissful coercion) used in the Matrix betas:
The Architect: The first Matrix I designed was quite naturally perfect, it was a work of art - flawless, sublime. A triumph equalled only by its monumental failure. The inevitability of its doom is apparent to me now as a consequence of the imperfection inherent in every human being. Thus, I redesigned it based on your history to more accurately reflect the varying grotesqueries of your nature. However, I was again frustrated by failure.
As Agent Smith notes in The Matrix, "entire crops were lost" while the Paradise Matrix was in use.