Luminiferous aether means light bearing aether (lumini - light, ferous - bearing or conveying) - a medium through which light propagates.
The origins of this theory were the experiments that showed that light behaves like a wave. Because all other waves propagated through some kind of medium, it was hypothesized that there must be a medium through which light wave traveled. The properties of this medium were unclear, and thus were debated throughout the 19th century.
To understand the needed properties of this medium, we must first understand the origins of the term aether. Then we will look at the history of light and wave physics, from which we will be able to understand the properties of the aether.