@Meerkat,
One of Swami Vivekananda's most favored disciples once approached him and Vivekananda said to him, "Ask something of me, and I will give it to you."
The student said, "I have listed to your lectures on maya and still don't completely understand what it is. What is maya?"
Swami Vivekananda stood silent, and after several moments, said to the disciple, "Ask me something else."
My point is that if a disciple of Sri Ramakrishna himself struggles to explain why maya is illusion, it will be difficult for most of us to explain as well.
The best way I've found explain that maya is (or more accurately does) is to consider what a dream is to you during sleep. During sleep, the dream is very real, and in most cases, all there is that is real from the perception of the dream. But upon waking, you know the dream is merely an illusion created by your mind, and your waking reality (vyavaharika) is what is real.
A realized person is one who has awakened from vyavaharika and has a stable perception in Paramartika (absolute reality) and knows vyavaharika is merely an illusion created in maya.