Maya (माया or māyā): In philosophy the word origin of maya is derived from the Sanskrit roots 'ma' ("not") and 'ya', meaning "that". So the meaning of Maya is "that is not" but which appears to be real. Maya is held to be an illusion in philosophy & it is said to be a veil of the true Self - the Universal Spirit known as Brahman. Maya is a subtle force that creates the grand illusion that the phenomenal world that we see is real.
Maya is said to be neither true nor untrue. Since Universal Spirit (Brahman) is the only truth so Maya cannot be true. Since Maya causes the material world to be seen, it cannot be untrue also. Hence, Maya is described as indescribable. She has two principle functions - one is to veil the Universal Spirit (Brahman) and obscure and conceal it from our consciousness. The other is to present and promulgate the material world and the veil of duality instead of the Universal Spirit (Brahman).
In the darkness, just like a rope is confused for a snake & this illusion gets destroyed when true knowledge of the rope is perceived in the light. Similarly, in the darkness of the night, a pole may be mistaken for a ghost. As the darkness is removed, the ghost disappears; only the pole remains as reality. Similarly, Maya's illusion gets destroyed for a person when he/she perceives Brahman with transcendental knowledge & light. When the light of Universal Spirit (Brahman) falls on Maya, it disappears.
Purpose of Maya: In reality the purpose of Maya is to produce the duality in this world. Maya performs this role at the behest of the Supreme Lord only. God is not bound by Maya, just as magicians are not illusioned and deluded by their own magic.
Maya is beyond our sense-perception & is invisible but this universe which is its effect, is visible (or perceived by the senses). Maya is like night (or darkness) & is very difficult to be understood. Its nature is not perceived here.
In Hinduism, this world in which we live is called unreal not because of that it does not exist, but because it is unstable, impermanent, unreliable and illusory. It is unreal because it is transient & changing every second. Just check the things around you, these are changing every second. So this changing world, which is not permanent is called Maya or illusion & not real, the changeless.
Lord Krishna in Bhagwat Gita details about the 'Maya' in it's various chapters.
"mama yonir mahad brahma
tasmin garbham dadhamy aham
sambhavah sarva-bhutanam
tato bhavati bharata" (Bhagwat Gita: Chapter Fourteen verse 3)
"Sri Krishna said: O Arjuna, My womb is the great Nature (Prakriti or MAYA) which is the source of birth of all living entities, and it is in that I place the germ (embryo of life). Thus it makes possible the births of all living beings."
"sarva-yonisu kaunteya
murtayah sambhavanti yah
tasam brahma mahad yonir
aham bija-pradah pita" (Bhagwat Gita: Chapter Fourteen verse 4)
"Sri Krishna said: O Arjuna, It should be understood that all species of life, are made possible by birth in this material nature (Prakriti or MAYA), and that I am the seed-giving father."
"yavat sanjayate kincit
sattvam sthavara-jangamam
kshetra-kshetrajna-samyogat
tad viddhi bharatarsabha" (Bhagwat Gita: Chapter Thirteen verse 27)
"Sri Krishna said: O Arjuna, Wherever a being is born, whether unmoving or moving, know that it is from the union between the field and the knower of the field. (Purusha is the knower of the field; Prakriti is the field; Shiva is another name for the knower of the field and Shakti is the field; Spirit is another name for the knower of the field and Matter (Prakriti) is the field).
"prakrityaiva cha karmani
kriyamanani sarvasah
yah pasyati tathatmanam
akartaram sa pasyati" (Bhagwat Gita: Chapter Thirteen verse 30)
"Sri Krishna said: O Arjuna, One who can see that all activities are performed by the nature (Maya) alone and sees that the self does nothing, actually sees." (The Self is the silent witness).
"ishvarah sarva-bhutanam
hrd-dese ’rjuna tishthati
bhramayan sarva-bhutani
yantrarudhani mayaya" (Bhagwat Gita: Chapter Eighteen verse 61)
"Sri Krishna said: O Arjuna, The Supreme God is situated in everyone’s heart, and moves them to act by his divine Maya, who are seated as on a machine, made of the material energy."
Ramakrishna on Maya
Ramakrishna acknowledged the power of Maya in life. He was all love and reverence for maya, perceiving in it a mysterious and majestic expression of Divinity. To him Maya was God.
In the guru Ramakrishna's experience, Maya was divine. Ramakrishna "did not, like a Vedantic scholar, repudiate the world as maya, but gave it a spiritual status, seeing in it the manifestation of Chit and Ananda." Ramakrishna had a "vision of the divine Maya, the inscrutable Power of God, by which the universe is created and sustained."
According to Ramakrishna, Maya projects and withdraws the world.
Further, "Maya . . . is the Mother of the Universe, identical with the Brahman of Vedanta and with the Atman of Yoga.
Ramakrishna discovered that maya operates in the relative world in two ways and he termed these "avidyamaya" and "vidyamaya.' Avidyamaya sustains lower planes, but vidyamaya is enlightening, including qualities like kindness. Vidyamaya elevates a man to a better consciousness. With the help of vidyamaya he then gets free of maya, if only for a while. The two aspects of maya are two forces of creation.
Ramakrishna said further: "When I think of the Supreme Being as inactive - neither creating nor preserving nor destroying - I call Him Brahman or Purusha . . . When I think of Him as active - creating, preserving, and destroying - I call Him Sakti or Maya or Prakriti, the Personal God.
To Ramakrishna maya itself was God - everything was God - [maya] was one of the faces of [the Godhead].
As per Ramakrishna: Maya can not be distinguished from the supreme [Godhead]
As per Ramakrishna: The mighty weaver (Maya) is none other than the Divine Mother.
As per Ramakrishna: Maya releases from bondage.
"I tell you the truth: there is nothing wrong in your being in the world." - Ramakrishna
Vivekananda on Maya
This universe is maya - Vivekananda
Maya is used incorrectly to denote illusion or delusion. - Vivekananda
Whether God is active or Inactive? To get the answer for it, here below are views of the great saint of West Bengal, Sri Ramakrishna.