The luminiferous aether must have certain properties in order to allow the propagation of light waves. Though these properties were uncertain and open to disputes and debates.
First, light must be a transverse wave in order to explain the phenomena of polarization. Transverse waves are waves that oscillate in a direction that is perpendicular to the velocity of the wave.
The orientation of the oscillations is the polarization of the wave. Linearly polarized waves oscillate in a specific perpendicular line, while circular and elliptical polarized waves move in the whole perpendicular plane.
Transverse waves, at the time, were only known to propagate through solids. Thus, it was argued that the luminiferous aether must have the properties of a solid, rather than a gas or liquid. However, it didn't seem that there was any interaction between the aether and any other regular matter, which posed a problem.
These hypothesized properties of the luminiferous aether were highly debated and weren't really understood. However, the essence of the luminiferous aether changed completely when James Maxwell showed that light wave were actually electromagnetic waves.