This experiment encouraged physicists of the day to invent explanations which agreed with both the experiment and existing theories. Two of the most popular were the "ether drag hypothesis" and the "emission theory."
The ether drag hypothesis claimed that the ether was attached to objects with finite mass. This theory was rejected because it predicted the absence of readily observable stellar aberration.
The emission theory modified Maxwell's equations such that the velocity of light depended on the velocity of its source. Emission theory was rejected because of its inconsistancies with the observation of binary stars.
Source:
Eisberg, Resnick. Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. Second Edition. Wiley, New York. 1985.