Out from the Deep Lyrics
To learn to love, to learn how to live.
To avoid the mistakes we made
That's why we are here
That's why we are here
To help and understand, but not to kill.
To clear the debts of many hundred years.
That's why we are here
That's why we are here
That's why we are here
That's why we are here
That's why we are here

Alright, b4 I begin, let me say that I have heard this song about 30 time minimum. It started making sense when I started learning about souls journey and weird stuff like that. Here is what I think...
"We came out from the deep" ... We are reincarnated from the spirit world into our world/planet of choosing. This planet could be earth or any other with intelligence lives for souls to bind with and take over.
"To learn to love, to learn how to live." ... soul journey to becoming more is that of learning and experience acquisition. I am much even touched by this coz i heard that being a loner may hinder ur evolutionary soul development.
"To avoid the mistakes we made" ... every reincarnation is a chance to live and try to overcome certain past mistakes in our past lives. So...you may need to learn more on how "...to love, to learn how to live."
"It takes many lives till we succeed." ... yes, it is said that soul development is reaaally slow. In some life time, u may not even learn much, an utter waste.
"That's why we are here" ... alright said already, we are here for learning and experience accumulation towards becoming like the source or something like God.

The songs starts off with dolphins' sound.
Out from the deep could refer to a new specie(of human) coming out nowadays: tamed yet virtuous like with the true (philosophical) ability to understand, learn, love and live (to avoid past mistakes).
This new generation of humans is emerging from all the deaths and (again) mistakes throughout history like wars and all deadly ignorance (All lives taken are the debts of many hundred years).
One of Enigmas greatest song and guitar solos at the end - quite exciting.

My take on the song is not as enigmatic (pun intended) as the others listed. I just rediscovered the song and find it haunting. And very catchy in its simple refrain.
My initial thought was that it was a pro-science song about evolution. We came out from the deep (the ocean) and we are here to learn to love and live - not hate and kill.
In regard to the references to the mistakes we made, our many lives and hundreds of years, my interpretation is that its a commentary on colonialism and our many wars. The many lives are many generations, and hundreds of years refers to how, as a species we are actually becoming less violent and there is less death, not more. See Pinkers' "Angles of our Better Nature" for detail on that.
I see how it's easy to read a very spiritual message into the words. They are somewhat vague because...well Enigma, right?
In sum, even if it were complete nonsense, I cannot get this tune and the catchy refrain out of my head. Ultimately, every person has to decide for themselves, why are we here? Ah, THAT is why we are here! Sing it again!
I M Probulos Author, Amazon, (over 30 books)

When I heard this after studying the ET and UFO phenomenon in depth, I think that this song may refer to the history of the greys ET's. We know ET's have underwater bases and we have understood that they have been involved in devastating nuclear wars leading to reproductive problems. They are comming here on earth to warn against the danger of nuclear armageddon, the abuse of earths natural resources as well as the addiction of humanity to technology which also leads to climate change. They've had these problems and they warn us against repeating their mistakes. It may take many lifes (meaning reincarnations) to learn the lesson, but they are patient. We need to learn to learn to live in harmony with earth for the human species to survive. That's why they are here...