The Breeding Program was a long-term project developed by the Bene Gesserit Sisterhood whereby certain genetic stock was purposefully bred. For more than 10,000 Standard Years the Bene Gesserit had manipulated bloodlines to produce the Kwisatz Haderach, essentially a male Bene Gesserit who could possess Other Memories as well as see into the future.
After it had been established in 10,191 A.G. that Paul Atreides was the Kwisatz Haderach, the Bene Gesserit breeding program continued. However, it was shortly thereafter usurped by Paul's son Leto II, and maintained by him until his death approximately 3,500 years after he took to the Imperial throne. Leto's breeding program was primarily concerned with the creation of an individual like Siona Atreides; one with the genetic ability to remain unseen by prescient searchers such as the Spacing Guild or Bene Gesserit. What other secondary goals Leto may have had (or even achieved) remain unknown.
Upon his death, the Bene Gesserit once again took control of the program. Through it they bred genetic lines into their own Sisterhood, and other areas. Their later efforts resulted in Miles Teg, among others.