artist's impression of the Big Bang

The word 'maya' is derived from the root 'ma' which means 'to measure', more specifically, to measure or lay out, as in a shape, a form, a thing, a something or other. In other words, every manifest form, from concrete building forms to peyote induced hallucinations, is an instance of something measured out -- out of the vast, unmeasurable unmanifest into definite form; into what Shakespeare calls 'a location habitation and a name.'
The designation of the realm of forms as 'illusory' creeps in when we begin to notice that the entire showing forth of things with measurements tends to draw a veil over the Oneness out of which all forms manifest. We get so focused on the forms that we lose sight of that which makes them possible in the first place.
When we forget the Oneness, we open ourselves to all kinds of dysfunctional involvements with forms, many of which produce that phenomenon we call suffering. We cling to forms, lust after them, flee from them, believe in them, fear them, grasp at them, kill them, die for them, swear allegiance to them, sell out for them, collect them, archive them, subject them to analysis; in the end, become completely dominated by them. Are we to blame for any of this, we who have nothing but forms shoved in our formed faces from birth on? If, as Hinduism holds, manifestation is the work of a Maha Shakti, a Cosmic Creative Agency that brings all form into existence, what chance do we puny humans have of seeing through Her Dazzling Display into the Divine Oneness out of which, and within which, every form, ourselves included, arises?

One of the best takes I've found on this rather important issue, is this.... To paraphrase the Indian sage, Sri Shankara, (circa 1200 years ago): The world viewed as separate from transcendent Divine Oneness is unreal, the world viewed as an integral expression of that Oneness is real. That, in a nutshell, is the real definition of Maya -- the world viewed as separate from Oneness, or, viewed without even noticing Oneness.
The irony is that we are so bamboozled by forms that most of us see the world as all there is and deny that Oneness even exists, because we can't see it. In Shankara's view, that's deep, deep Maya.
afterthought: Even to call it Oneness is misleading. It is not a big ONE out of which a whole bunch of little separate things tumble. Such a ONE would just be another thing, albeit the biggest most inclusive thing. Rather, Oneness or 'Beingness' as Henri Corbin calls it, is beyond duality, beyond enumeration, beyond distinctions we make between this and that. This Beingness is infinite beyond comprehension. Its infinity is in its smallest parts as much as in its overall incomprehensibility -- because, if you think about it, that's what infinity means. It is conceptual distinction-making that labors to lop off the infinite. Or, as Vedantic scripture puts it, "Daily we dismember Brahman."
The irony is that we are so bamboozled by forms that most of us see the world as all there is and deny that Oneness even exists, because we can't see it. In Shankara's view, that's deep, deep Maya.
afterthought: Even to call it Oneness is misleading. It is not a big ONE out of which a whole bunch of little separate things tumble. Such a ONE would just be another thing, albeit the biggest most inclusive thing. Rather, Oneness or 'Beingness' as Henri Corbin calls it, is beyond duality, beyond enumeration, beyond distinctions we make between this and that. This Beingness is infinite beyond comprehension. Its infinity is in its smallest parts as much as in its overall incomprehensibility -- because, if you think about it, that's what infinity means. It is conceptual distinction-making that labors to lop off the infinite. Or, as Vedantic scripture puts it, "Daily we dismember Brahman."