This character is Gilgamesh's mother and a goddess. She prays for Gilgamesh and Enkidu and their well ending as warriors against Humbaba. She is also called the Lady Wildcow Ninsun. She is a minor goddess, everyone respects and loves her for her wisdom. Her husband is Lugulbanda. Talking about Ninsun, we can give a piece of advice – you may take any advice from this lady, really. Below you will get it why. At first, let’s see in details what her character is about.
Lugalbanda, Gilgamesh's father, was a simple mortal human. He was dead extremely before the epic begins. Much like Thetis (another goddess who appeared in Homer’s Greek epic “The Iliad”) she is devoted to her son the same way. During all the story she tries to help him every time he needs it or not. Well, we can see her character very good when she comes to Shamash (the sun-god) to ask for her son. She did it before her son and Enkidu were going to the fight with Humbaba. As a result of their dispute they understood that they would need the help of Shamash – and here the mom is, saying that she did it already.
Also, we can’t perceive Ninsun as just a typical mom who cares a lot about her child. She was also very hot. While reading the story, you can see phrases like "a robe worthy of her body" and "jewels worthy of her chest"… do you know to whom was she going to wear all those stuff? No? To Shamash. That is why we can make a summary that she knew what her strong sides were and how to use them properly to get results.
She was always scared not to give her son all things she has, though she was very sad when she got to know her son has such a bad behavior and that is why she wasn’t against Enkidu (she was even happy that there would appear a guy who will teach her son that things don’t work like that, even if you are a king). This means she was fair.