I can speak from personal experience. I have been on an enlightenment intensive. I could give a very detailed description of the progression I went through. However it is quite impossible to explain the state of 'knowing' that one achieves.
In normal life we experience the world through sensation and we have beliefs about what we haven't sensed. The sense of knowing is quite different. It is not a strong belief, it is not faith, it is absolute knowledge.
You may ask what does someone know in this state. In my case I knew my oneness with the universe. What does that mean? It is not an intellectual understanding, it is an experience of being the universe rather than being part of it. There is no way to explain it.
By the way, although I remember what it was like, as I write I am not in that state. I do however know that is attainable again if I so wish.
The state is as far from being delusional as it is possible to be.
I don't think that psychology could even remotely deal with it because psychology is an intellectual discipline dealing with evidence. The state of enlightenment (or whatever you want to call it) is neither intellectual nor does it require evidence.
For me the state lasted for a few minutes at a time. I was scared to allow myself to go deeper and I pulled back. One day I may go on another such retreat and allow myself to experience it fully.
Note that this experience is available to pretty much anyone. I can't remember who ran the course I went on, it was a long time ago, however you can find enlightenment intensives online.
By the way I have a science and maths background. I am pragmatic by nature and very down-to-earth. I do not subscribe to airy-fairy new age type beliefs. I am also an agnostic. An enlightenment experience is not dreamlike or wishy-washy, it gave me the most clarity that I have experienced in my life.
I recommend it to anyone.
(Please feel free to ask me any questions)
I guess that the nearest that science could come to this would be to brain scan someone who was experiencing the state. I'm sure it would be entirely possible and, I think, very interesting. I would be fascinated to know which brain areas were doing what.