What the leaders of the brave new world are trying to do is to make it so that everyone in the society (and especially within each caste) will be as similar as possible. They want people to be the same, in part, so there will be little to no conflict between people and the society will be completely stable.
That is why the Bokanovsky Process is such an important instrument of social stability, especially for the lower castes. By creating people who are completely identical the leaders of the society can make the people as identical as possible. When people are identical, at least according to the book, they will respond in the same ways and will not come in conflict with one another. As the Director says:
Standard men and women; in uniform batches. The whole of a small factory staffed with the products of a single bokanovskified egg. "Ninety-six identical twins working ninety-six identical machines!"
The Bokanovsky process is important for social stability as envisioned in the novel Brave New World. The purpose of this process was to enable the government to control the population and the functions of the people in society. This process was specifically used for the lower caste of the society as established in the novel. It involved human cloning where the genetic makeup of the individuals born was identical. The process produced identical sets of clones with different features between the sets. The reason for this was every set had a specific role to play in the society. The clones working in different environments had to have different adaptations. For instance those working in the foundry had to be heat-conditioned.
In summary, the Bokanovsky process as applied by the government was envisioned to cultivate a stable society that functions efficiently.