A rough try:
The dictionary definition is 'an age' or 'a lifespan.' As understood within Thelema, it is a particular period of time characterized by a certain ruling current or general characteristic(s). These characteristics are summed up as comprising the effective direction of a particular god, which we interpret according to a specialized (not necessarily historical) understanding of some of the Ancient Egyptian deities.
In a practical sense, Aeons are understood as phases of evolution of human consciousness, where the different parts of the spiritual psyche are awakened and activated.
My own take is that we have come from primitive survival in the Aeon of Isis (the nephesh/animal soul becoming active in the guph, or body); to awakening awareness in the Aeon of Oriris (nephesh feeling the impact of ruach, the self-conscious or ego awareness, and we humans thus differentiating into selfhood); to, in this Aeon, fully awakening ruach under the impact of neshamah, the supernal consciousness.
Other people might care to refine that simplified description.