One of the great mysteries of the series was the island. We know a lot about the island, but we really don't know a lot of important information about the island.
One thing we do know is that the island is hard to find, even with the most advanced technologies. Therefore, the island is a "closed" system. It has a special barrier that limits who can ingress or egress its boundaries.
During the family feud, Jacob's brother killed Crazy Mother, and then Jacob killed his brother (which was strictly forbidden). As a result, a smoke monster took the form of his dead brother (MIB). It appears that they were to live alone on the island forever. Jacob was given the role of island guardian, and MIB was given the role of island security dog. But if no one could find the island, their existence would have been futile. Without MIB presence, Jacob probably would have gone mad in isolation (which was probably what happened to Crazy Mother).
We know that the unique energy of the island is contained in the heart of the island, which equates to some kind of "life force." The light source was described as "life, death and rebirth." The context of this description is that the heart of the island is the heart of the universe - - - the creator of all life and the religious recycler of all death into new life.
So we know the importance of the island as it houses the power to create life, destroy life and re-create life.
To save his own sanity, Jacob decided to bring "candidates" to the island in order to a) play a game or b) experiment with human behavior to prove a point to MIB. We know that deep inside MIB's memories is the strong desire to "escape" the island (as Jacob's brother did), so MIB played along with Jacob's work. MIB's support of Jacob bringing people to the island was a mere ploy to learn how to get off the island. If MIB could not directly kill Jacob (as was the rule with his brother), then MIB would use trickery to get one of Jacob's candidates to do it. MIB frustration with the people brought to the island was clear: they would get her, settle in, then devolve into "corruption." From MIB's perspective, corruption could have been worship of Jacob and not plotting his demise. From Jacob's perspective, the people brought to the island did not get the result he secretly wanted: death and release of his responsibilities as Crazy Mother had lured Jacob into thousands of years ago. Even though they did not know it, both Jacob and MIB were looking for the same result but took their own different paths to try to achieve it. This caused a frustrating stalemate.
Since the candidates were brought to the island, they were under the sphere of influence of the heart of the island. We do not observe any intelligent behavior of the light source itself. We do not observe it changing or killing either Desmond or Jack when they went into the light cave to reboot the island. Whether Dez and Jack were marked with immortality earlier by the island is unclear, but whatever they did together did set the stage for the final time of Jacob and MIB.
The light source had to transform the candidates into one of the three categories: giving life, giving death or giving rebirth. We know that all of the candidates and their closest friends were reincarnated in the sideways church world, a place in the after life. The exact process of that reincarnation is unknown. It appears not automatic, as there were several candidates who were either trapped on the island as spirits or never made it to the sideways world.
As a machine diagram, the island looks like it takes through its barrier human souls, experiments with them in order to either remold or change their behavior, then releases them back to their lives, or kills them directly, or gives them rebirth either on or off the island.
