I have heard that when a meditator does a long meditation, he is able to enter into different world, see and hear that world. What are those? Are they just illusion, imagination or different universe?
In Pali Buddhism, the word 'world' ('loka') refers to different mental states.
For example, MN 79 calls the meditative jhanas of pure bliss 'the world of only pleasant feelings' ('ekantasukhassa lokassa'). To quote:
Venerable sir, what is that course of actions to realise the world of only pleasant feelings?
Here, Udāyi, the bhikkhu secluded from sensual desires and thoughts of demerit abides in the first jhana: Overcoming thoughts and thought processs and the mind in one point internally appeased, without thoughts and thought processes abides in the second jhana. Again with equanimuity to joy and detachment, feeling pleasant with the body too, abides in the third jhana. To this the noble ones say abiding in pleasantness with equanimity. Udāyi, this is the course of actions, for realising the world of only pleasant feelings. `
'Nibbana' is not a 'world'. The attainment of Nibbana is the 'cessation of the world', which is experienced within the living body & mind. To quote:
There is, bhikkhus, that [sense] base where there is no earth, no water, no fire, no air; no base consisting of the infinity of space, no base consisting of the infinity of consciousness, no base consisting of nothingness, no base consisting of neither-perception-nor-non-perception; neither this world nor another world nor both; neither sun nor moon. Here, bhikkhus, I say there is no coming, no going, no staying, no deceasing, no uprising. Not fixed, not movable, it has no support. Just this is the end of suffering. Ud 8.1
Within this fathom-long body, with its perception & mind, that I declare that there is the world, the origination of the world, the cessation of the world and the path of practice leading to the cessation of the world. AN 4.45
Therefore, when a meditator does a long meditation & is able to enter into different world, those worlds are not just illusion, not imagination or not a different universe. Those worlds are mental states.
As for Nibbana, this is also not illusion, not imagination & not a different universe. However, it is also not another world and not a mental state, even though Nibbana is experienced by the mind.
What is called world in Buddhism is the six senses. When you meditate you experience finer senses which you can't experience via ear, nose etc. When you meditate you experience finer wholesome mental states. The logic here is for example you can see only colours from your eye. Even if you become a Deva or Brahama with your eye you only see colours.
A meditator doing long meditation is able to enter into a different world. We call this the entering into a Manomaya Kaya or that of an Out-of-Body Experience. The Buddha compared the situation of a manomaya kaya separating from the physical body to a sword pulled out of its sheath, or a snake shedding its skin. Once the manomaya kaya comes out, the body is lifeless like a log. The life force or the vitality goes out the moment the manomaya kaya leaves the body.
When the manomaya kaya and the physical body separate, “seeing” takes place without the need of light. The person acquires the ability look at things far away. Ones “hearing” then does not need air as a medium for the sound to propagate (one could hear things far away). “kirana” or “rays” similar to electromagnetic radiation helps in this ‘hearing’. One also gets to “travel” very fast; it is not physical travel. The Buddha or Arahants with iddhi powers travelled to the worlds of the devas (deva-loka) within a time taken to “stretch a bent arm”. The internal eye and internal ear associated with the manomaya kaya helps in the actual “seeing” and “hearing”.
Okay. It has been scientifically proven that the brain cannot distinguish between you imagining a situation and you actually being in a situation.
So when you meditate with the aim of being detached from your experiences you'd also detach yourself (your soul) from the ego perspective of being in the situation imagined or real.
So the world you'd be a part of then is the soul world.
Now the term out of body experience would say that you actually leave your body, which is not really the case. You just focus on other input that you can receive, mostly via the third eye and other sensations that directly touch your soul.
Since the soul is eternal, yet the body isn't you'd be able to experience everything that your soul has, is or will be experiencing.
If you follow that and say that the soul was there before the body that means the soul is on the inside and the body is on the "outside". So you'd actually be venturing inside by not being attached to your bodies experiences anymore.
However. As long as you(your body) is alive you will never completely detach, so there are always some signals coming through. You just focus on the other ones more.