According to the Advaita philosophy, this world we live in, the space as well as time is a projection of your consciousness or your awareness. In fact your mind, your thoughts as well as your physical attributes are just a projection of that consciousness into the state of waking. Advaita Vedanta calls this projection as Maya. Maya creates apparent multiplicity in a universe where only Brahman really exists.
The true meaning of Maya in Sanskrit is illusion or delusion. Advaita Vedanta uses this term to bring forth a point that what we feel as real is not the complete reality. This does not mean that all of us live a life of illusion – we actually see it, we really live in it. “The world has no existence” really means “The world has no existence-absolute”. It only exists relative to our minds. It is perceived by us, by our five senses. That is what is meant by the “no existence” clause. It is a mix of existence and non-existence. This is Maya. It is the projection or manifestation of the Infinite through our finite minds.
Everything that has form, everything that calls up an idea in your mind, is within Maya, for, everything that is bound by the laws of time, space, and causation, is within Maya. And that includes the Vedanta philosophy, the philosophers, everything. Stretch your imagination as far as you can, make them higher and higher, call it infinite or by any other name you please, even that idea is within this Maya. It cannot be otherwise, and the whole of human knowledge is generalization of this Maya, trying to know it as it really is.
Understanding Maya, which is the world or the System we think in, is not a trivial task.
In fact, understanding any system from within the system is not possible - physically as well as mathematically. The great mathematician Gödel postulated this in his “incompleteness theorems” in 1931. In simple terms his theorem states that "This theorem cannot be proved!". By proving or disproving it, using any mechanics within the “System of proving”, you prove it. Essentially it boils down to the fact that in order to fully understand a system you cannot be within that system - you need to be outside of it.
Study of something that you know at the onset that you cannot fully comprehend is an extremely difficult task. The only way to approach that is to equate it to the known; equate it to something that is “equate-able” from our point of view. So let’s then try and understand Maya using what we see around us and/or using something which is within the realm of our comprehension and then extrapolating it.
Extrapolation using our understanding of space:
We can all agree that, from common sense, that we all live in this 3-dimensional world where any single point – any single being/thing/atom/etc. can be identified by the 3 co-ordinates: x, y, z. Add to that the factor of time and you can precisely calculate a position of a point at any particular time.
Now imagine our 3-dimensional world made up of an infinite number of "2-dimensional worlds" that are perpendicular to the ground. If you have difficulty imagining that, imagine a number of walls of thin sheets front of you – so thin that they don’t have any thickness at all! Now imagine people in our 3-dimensional world moving through these various 2-dimensional worlds. Every time you walk, you walk through these 2-dimensional worlds – just like a ghost would walk through walls in our world.
We move through these 2-dimensional worlds in an instant but imagine that that instant is actually a really long time within the realm of the 2-dimensional world. Instances of people in the 2-dimensional world see this as birth and death of the instances of other "2-dimensional people". They rejoice and they mourn. This is their Maya. But we, in the 3-dimensional real world know the "truth". The instances of people in the 2-dimensional world are nothing but a projection of our 3-dimensional bodies when we pass through their 2-dimensional worlds.
Extrapolation using our understanding of thought:
Another scenario that can be considered is using the planes of thought (just like we considered the dimensions in space in the last example). Think of dream as one of those states. When in a dream, everything in the dream feels real. When in a dream there is no concept of "outside-the-dream". Think of that as the Maya of that plane. But the moment you wake up, you go to a different plane of thought. Of course you do not change your physical location with respect to space and time (if you were sleeping on your bed, you wake up in your bed) but your thought, your consciousness, your awareness, moves to a different plane where you realize that the dream was not real and the waking state is the reality. You, in the woken-up state, understand the triviality of everything in the dream state including your feelings (fears, sorrows, joys); just like you in the 3-dimensional space understand the triviality of the sorrows and joys of the people in the 2-dimensional space.
Ah! So I can have my own way if everything is in-fact unreal…
Advaita says that the world of Maya is “un-real”. But that does not mean that we, within the world of Maya, can have our own way around everything. “Let me steal since in any case this is all un-real!”. That is not the idea here.
Maya may be “un-real” from a grander viewpoint, but from within Maya things are very much real. So if you want to take “advantage” of the fact that everything around you is Maya and you can have your own way, you need to evolve beyond Maya. But then what will you take "advantage" of; when you realize the illusion itself!
One obvious question is what exists beyond Maya? Advaita says that an “Absolute” is the reality. Maya is just the manifestation of this Absolute and this Absolute is the pure consciousness, pure awareness. This absolute awareness does not limit itself to any individual – it is the collective absolute awareness. This absolute, totally impersonal, ultimate reality is the Brahman.
Then the obvious question is what created this Brahman – the pure consciousness. Vedantists say: “We will answer this about the Brahman if you ask the right question!”. This is not an arrogant answer – it just brings forth the fact that there is no right question to address this inquiry. That is because the Brahman is beyond causation. This may be a difficult concept to grasp but the Brahman just does not have the same attributes that objects have in Maya – it is in a completely different plane of awareness. You cannot use the same attributes that you are aware of in this System and apply them to another System. Just like the 3rd dimension is an incomprehensible and inapplicable attribute for people in the 2-dimensional world – the systems themselves are different – you cannot take the attributes in Maya (space, time, causation) and apply them to the Brahman. In fact consciousness too is not an attribute of Brahman but is its very nature. There is no cause for the Brahman because causation is not an attribute in the plane of the Brahman; space and time and causation do not make sense in that plane and relativity breaks down. It is the Absolute.