This is how I explain it

 If we can accept that consciousness is at the basis of all things, including us, and that consciousness, in its most fundamental definition, is "All That Is", it follows that we are always part of this consciousness, right now.... on the physical level, on the level of the mind and on the "super-mental" level (the level that transcends and includes the mind and the body). 

This point of awareness that we call "I"....where is it?

The first reaction of most people is "Here, this body. That's me."

Where exactly in your body?

Well...here, in my eyes...in my brain!

Can you pinpoint the exact location?

Ok, maybe it's not the brain but the mind. That's where the "I" is. Memories, thoughts, feelings, likes and dislikes....that's me.

But when you were born, you didn't have any of those. Was it still you?

Well, of course it was me, but.... errr, I don't know....

If I take away all your memories right now, will there still be a "you"? Or will you slump down dead like a sack of potatoes? Feelings come and go. You see them rising, you see them falling away. They appear on the screen of your consciousness. The same with thoughts. You are the "I" that observes them all.

Now it gets interesting.

So where is this "I" that comes before the first memories, thoughts, feelings?

In meditation I strive to first relax the body, then the mind. The mind is then prepared like a horse. I put the mouthpiece on, the blinders and hold the reins. Everyone can do it. You train your mind to stay focused on one thing and not fall pray to the wild monkey thoughts. Every time a monkey takes hold of you, you simply come back to your anchor, which in my case is a mantra, but can be a multitude of other things. And so, the monkeys will come less frequently and finally leave you alone. What you're left with is a calm, open mind...and silence. This state of mind is the best conductor towards revealing the true "I". The rational mind is not at work here. The true "I" lies beneath the mind, behind our thoughts, memories and feelings. This must be practiced and experienced first-hand. It can not be understood on an intellectual level, because the mind is the very thing that covers the observer behind it. When the mind subsides, the observer becomes stronger and we are able to widen our perspective (climb the tree trunk). 

For those rare people that have taken this to the final stage, a radically different world becomes evident. They may appear the same on the outside, but their "I" identification is no longer in the body-mind, they are now speaking from the perspective of the One Consciousness. "I" is for them the One Consciousness. 

To come back to enlightenment. What is meant by enlightenment is simply that first moment when consciousness realizes (remembers) itself completely and permanently. You can have several mystical experiences, many insights and awakenings before, but those are not permanent. You cannot be "un-enlightened" however. And why would you? You can still chop wood and carry water, while effortlessly resting as that One Consciousness.

I don't know if this is how Vedanta or any other philosophy or religion explains it. This is how I explain it.