Asymptotic equipartition property (AEP) is like having equal amounts of something in the end. Think of it like a game of musical chairs. Even though one person might start with more chairs than another, if everyone takes turns playing the game for a long time, eventually everyone will have the same number of chairs.
AEP is similar in that it's a mathematical law that predicts that if something is allowed to change over and over again over a long period of time, then the situation will eventually look the same no matter where you start. For example, if you looked at the energy of a system of particles after a long period of time, the AEP says that each particle in the system will have an equal amount of energy, no matter how much energy each particle had originally.