When two species occupy the exact same niche, there will be competition. There is usually a set amount of resources in an ecosystem, so when two species need the same resources, or occupy the same niche, there will eventually be competition.
Competition will lead to one of the species outcompeting the other one. Although this may be a long process, the more resources one of the species obtains, the more they will reproduce.
This is the exact opposite for the other species, they cannot obtain resources due to the other species, so they will start to die off.
Due to both the competition of resources and the lack of reproducing, the species that cannot obtain their niche likely will die off completely or become very scarce.