The easiest way to explain enlightenment is as a mental state devoid of preconceived notions and psychological projections. This means that things are exactly what they are without regard to your relationship towards them. You just look at things and see them.
The onset of enlightenment is often equated with an "Ah-Ha" or "Eureka" moment. In fact, the second Buddha ever is said to have reached enlightenment after watching the first one hold up a flower.
The first Buddha was supposed to be giving a speech to a group of people but instead of preaching and talking, Buddha just held up a flower, a move which went over most people's heads. Only one person in the entire crowd "got it". He understood the unspoken message of Buddha and was "instantly enlightened " according to most accounts.
Buddha Two (Electric Buddhaloo) just understood that words are kind of silly, and the way to Buddhahood is just to see the flower without bothering it. He also understood that the flower is a metaphor for reality.
Ideally, one should look at everything the same way that the Buddha suggests we look at the flower. That is to say, we should look at and experience life without trying to bother it by telling it what we call it. Like we mentioned in the first paragraph.
...and don't come back until you can remember where you parked your car.
It's not that easy. If it was, this blog and billions of books wouldn't need to exist. Trying to explain it is not that important either. Enlightenment, like spirit contact and the development of psychic abilities, is something to be acknowledged, accepted and filed away. In the Zen way of looking at things, it's just another by product of meditation.
There's no way to accurately describe the enlightened state with words because the whole point of it is to negate the effects of language and just be.
You can't teach someone how to become enlightened, it's just as pointless as trying to explain it. That's why Zen doesn't try to explain or teach some lame method for attaining it. What it does do is to try and short circuit a person's thinking patterns so that they might experience the enlightened state for themselves. Once experienced, the focus shifts to maintaining this state of awareness permanently.
Sustaining this perspective is the meat and potatoes of Zen philosophy. Where other traditions focus on the bells and whistles of unfolding consciousness, Zen is happy just to be.