From the instructions:
Player #1 represents the investigators who have witnessed strange murders on the Miskatonic University Campus and now seek to find and destroy the cause of these murders before greater evil befalls Arkham. The evil is the spawn in human form, Wilbur Whately [sic]. To win, the investigator player must find and destroy him before or after he transforms into the spawn.
Player #2 represents the spawn and the cultists that worship and protect him. This player must eliminate all professor, police, reporter, and detective counters from play. At any point that he achieves this goal, player #2 wins the game. In the process of this, player #2 attempts to have Wilbur kill enough people to gain the energy he needs to transform into the spawn. Once Wilbur is the spawn, it will be much easier for him to attack and win.
Wilbur must transform into the spawn by the end of the last full moon phase on the turn track or his opportunity will pass until next year. Should he fail to transform into the spawn by the end of this phase, the game ends in a stalemate.