The Golden Path was an expansive prescient interpretation that was only visible to the Kwisatz Haderach. It foretold the fluid events of the future, both great and small. More profoundly, however, it revealed an optimum path through the countless threads of cause and effect that were encountered by the human race.
Through prescience, Paul Atreides and Leto II foresaw that humanity would end if it remained confined within the known universe and rigid class structure of the Imperium. Though the Imperium's population was many trillions, Leto II's rule proved that humanity was still confined within a space that could be controlled by a single interest. Although rarely addressed directly, it was often suggested that this lack of exploration and growth would cause the eventual destruction of humanity. The conflict between humanity's stated desire for peace and their actual need for volatility was the central theme of the entire Dune series after book one. God Emperor Leto II's stated goal was to "teach humanity a lesson that they will remember in their bones". That sheltered safety was tantamount to utter death, however long it would be delayed.
Origin
Though the Bene Gesserit had long anticipated the existence of The Golden Path, the term was first vocalized by Paul Atreides after the defeat of House Atreides on Arrakis. However, its inherent dilemmas were only apparent to him after he ingested the Water of Life. Even with his considerable powers Paul struggled to determine the best path through the maze of decisions presented to him. This was possibly due to the fact that he was not the ultimate Kwisatz Hadarach, having been born a generation sooner than the Bene Gesserit had planned. It was more likely, however, that Paul's difficulty with maintaining a clear oracular vision was because of his own emotions. Much like his father, Paul was forever tempted by a simpler life, far away from the intrigues and dangers of prescience, imperial politics, and war. He was also continually haunted by the death of his father, and the manner in which his House was betrayed by so many.
Evolution
After Paul's apparent death in the deserts of Arrakis, his son Leto - also technically a Kwisatz Haderach - began to see The Golden Path, albeit with more clarity and distance than his father. Leto's ability to see further and deeper into the threads of causality allowed him to craft a future in which he became a human-sandworm hybrid, and thus the long-lived God-Emperor.
In this form he guided humanity with an iron fist for three and a half thousand years, and used his own death to take The Golden Path even further.
At first The Golden Path appeared to culminate in the ascent of House Atreides, jihad, the spread of Fremen customs, and the terraforming of Arrakis. However, Leto extended it to incorporate an expansion in the diversity and safety of the human race, via The Scattering.
Ramifications
Despite the death of the two men who had enforced The Golden Path, its effects and ramifications were obviously still felt beyond the return of the Honored Matres and their eventual merger with the Bene Gesserit. Indeed, The Golden Path saw humanity explode across the universe, taking with it what it had known, and returning with it knowledge and technology never before encountered in the Old Imperium. Moreover, The Golden Path saw humanity's physical attributes change, so that their reflexes, nervous responses and physical movements were significantly faster than during the time of the Faufreluches.
Behind the scenes
The "great enemy" that threatens humanity in Leto's visions is not discussed in great detail. Herbert makes vague references to visions of future-time strands seen by Paul and Leto II wherein humans are fleeing machines, possibly of Ixian manufacture, designed solely to seek out and destroy human life. A future containing that fate would be the type of future that would compel a prescient Leto II to take humanity down his Golden Path, i.e. enforced tranquility, and accept his own fate of returning to the sand.