It is very hard to give you a good explanation here for those reasons:
- Sumerians myths are old, very old, de facto they are (and will probably stay) the actual oldest writings made by human beings, which makes them hard to access.
- Sumerians myths are difficult to read, I often (very) insist on that point. One has to see that human beings was learning to write. And it took time to see human beings fully mastering writing. Not that Sumerian writers was bad, they was not, they was just subtly bad.
- Most myths come way too incomplete. Try to imagine watching the Empire Strikes Back in 3017, but when Darth Vader is approaching Luke, he says: Luke, I... and the movie stops there. That what are Sumerians myths. We are missing, the puns, jokes, reference, culture and sometimes part of the text.
- The modern world is the heir of the monotheisms (Jews, Christians and Muslims). The proximity between this particular myth and the Genesis is quite stunning. Enough to guess the Genesis's root are something by there. Hebrews was never in contact with Sumerians. Sumerians was long history when the Genesis was written (around 1500-1400 BC). But Hebrews was knowing Sumerians myths via the Canaans. There is a quite subtle side effect here. Any modern reader reading the story of Ninhurshag and Enki will see it through the Bible's Eden lens.
The myth of Ninhursaga and Enki is a pure myth of creation. From the point of view of a society who need irrigation for surviving, as Egyptian by the way. You can compare with Indian myths (another river civilization, with lots of rain) or Mayan myths (a rain civilization with irrigation in mountains zone). Enki, the Sumerian God of water (he is the wise Ea in later Mesopotamia, and he is known as Ea as far as the Hittite) is depicted having several time sex and children with various women. The first being Ninhursaga, the Sumerian Mother Goddess (Call her Gaia in Greek myths, Xmucane in Mayan myth). They got a girl Ninsar the Sumerian goddess of vegetation). Enki seeing her has sex with her. One could see here incest in action which is obviously not the case. That is simply: When you pour water on ground, you have plants. When you pour water on plants they grow. This little game is going on a moment with Enki voraciously having sex with his own offspring (Ninurka, the mountain goddess), Ninimma (the goddess of female sexual energy) and finally Uttu, the destiny goddess not to be confounded with Utu the sun god, brother of Innana. I invite you to compare this section with the Genesis version which is basically quite near.
The first thing to see here is the all importance of Enki, creating gods after gods. As well as his strong sexual appetite. Part of the following up of this myth will resolve in a form of blame of Enki when he tries to (and factually does) mate with Uttu. You can especially takes a look at the approach Enki is using bringing a cucumber, and apple and some grapes (all more or then related to a form of sexual symbol). If you take by the way, a look at the Genesis version, the infamously renown "apple" is never mentioned, it is a "fruit". Here you have an apple. Try also to see the simple form of the story: bring me an apple and we have sex! That is a porn movie story. A lot of myth would fall in a way or another in this pattern, but that says something anyway.
This is where Ninhursaga will curses Enki, for eating his offspring with Uttu. What you have after that is your pretty typical rebirth myth. From the point of view of agricultural society rebirth is quite easy to understand: take a seed, put it in the ground and a new same plant will eventually rise. And that is why Ninhusaga is naked and places Enki under her vagina. Hope that is making sense.
One thing to see is: Myths do not try to give you any form of moral, or lessons about behaviours. They teach us more elemental things. Those old myths are also devoided of any form of psychology. What think Enki? What is the opinion of his daughters. There is no sense yet of authorship. Of psychology of characters. Human being will need to wait for Homer, some 2000 years, for such things.
You have also the "epic journey" of Enki which starts as a god obviously governed by his sexual energy and finish after a rebirth as a wise god (and will stay the Mesopotamian's wise god for a long time). Note also that the Mother Goddess participate a lot in that elevation.
What you have here so is a story about the origin of a cursed status of the human nature. For his appetite (for sex, or knowledge, and more probably for not refraining his sexual appetite and overdoing) Ninhursaga curses Enki. Quite similar to the way Adam and Eve are roughly punished by God for being over zealous about the forbidden fruit. Role of an external element is emphasized via either a fox (Enki's story), or a snake (Eden's story). In both case this lead to an immortal god (a Sumerian dingir exactly) to lose his life an being reborn, or human beings to become mortals. Understanding the similitude is a great way to be aware of the fact we have a terrible lens over our eyes.
One last point you can see there is the "over doing it" theme. Ninhursaga does not seem to react about the "inconstancy" of Enki until the moment he goes with Uttu. One of the subtext here is: it is not because you can do it, you should. Factually nothing stop or restraint Enki to keep going mating every female around him after this story, and considering who is Enki after we can bet he stopped (at least this story implies it).
Some people love we talk about modern myth: In Star Wars the 2 fights between Luke and Darth Vader are reverse. In the Empire Strikes Back, Vader has the advantage and even if he is not trying to truly kill Luke he still beats him, and very seriously. Compare with Luke's attitude in the Return of the Jedi where he has the upper hand and does not even truly try to fight. When pushed by anger he unleashed it he completely obliterate Darth Vader. Which illustrates that: it is not because you can do it, that you should do it. If, undoubtedly, this is a full Christian thematic, a part of that knowledge and theme are way older.