He is the mastermind behind the entire plot of the game: the unexplained deaths and the nightmares occurring in unfaithful young men. Though rumors surrounding the deaths say that each period of deaths occur in cycles of 100 years, this is not completely true, as Dumuzid made reference to causing the birth of Vincent by splitting his mother and her lover apart, so she could start a family with someone else.
Astaroth employs Dumuzid (Thomas Mutton) to target what he calls the "lowest of the low": men who cheat, betray, exercise deceit or are not fully committed to establishing a family and procreating with their significant other. These men, he claims, are taking someone else's future for their own selfish and immature reasons.
He communicates to all the chosen "lambs" through the Confessional on each Landing. Through that, he asks each sheep a series of questions that is designed to identify the true life's worth of the man. Though early in the game he claimed to only be watching over the sheep, he takes full responsibility later on for the entire series of events.
Though the entire trial exists to weed out unfaithful and uncommitted men by killing them in their dreams, Astaroth seems genuinely pleased and proud when Vincent survives all the trials. This act of baptism, as he calls it, is another reason the trials exist: to find the Man of Legends, and reward his potential.
Though never shown in the real world, Astaroth still has power over it, as he is able to block the memories of the chosen men so they will not remember the nightmares. He also communicates with Vincent specifically at the Stray Sheep, showing him visions of the next night and urging him to come into the dream world. Whether this is done for all candidates or because Astaroth suspected Vincent is the "Man of Legends" is not known.
Though a great deal of explanation is given regarding the reason for the nightmares and weakening deaths, in the opening movie to the Axis Mundi Babel stage, Trisha explains the whole purpose was just to find another consort.
If the act of forcing re-population in a world that is most likely already plenty populated can be seen as pointless at best and irresponsible at worst, one must remember fertility and re-population is the sole reason Ishtar exists.