In the anonymous epic of Gilgamesh, Enkidu serves as a moral compass for the young ruler of Uruk. Gilgamesh, as we first see him, is an example of absolute rule untempered by any sense of responsibility. He cares for no one but himself and nothing but his own pleasure. Enkidu, with his close connections with gods and nature, has not been corrupted by luxury. He is described in Tablet VIII:
Enkidu, . . . your mother is a gazelle,
and . . . your father who created you, a wild ass.
[You were] raised by creatures with tails,
and by the animals of the wilderness, with all its breadth.
In his friendship for Enkidu, and his mourning at the loss of Enkidu, Gilgamesh gradually develops a sense of empathy with his subjects and attitude of responsibility as a ruler. His experience with undergoing suffering and deprivation and his understanding of mortality in his quest after the death of his friend make him a wiser and juster king.
Throughout much of Gilgamesh's journey, we can see that, like any other human, this king has flaws and desires. One of his main desires, as the son of both a human and a god, is to find a way to reach immortality. (His mom was the minor goddess Ninsun, and his father was a King, and somehow this adds up to him being 2/3 god, and still mortal. Don't look at me, I didn't do that math.) In fact, we see a lot of rage from Gilgamesh toward the fact that he is mortal. As the King of Uruk, he is a terrible ruler—so focused on himself and his desires that essentially nothing else matters. He is disrespectful, violent, and apathetic.
Usually, when we in the modern day think of heroes, we think of the good guys, selflessly putting their lives on the line for others. Gilgamesh is a literary "hero" because he goes on a journey that has many of the classic elements of a literary hero's journey (meeting with a goddess, supernatural aid, etc.). When we say Gilgamesh is a hero, we don't mean that he's a good guy. At least, not until he meets Enkidu.
In fact, Enkidu was specifically made by the gods in order to help get rid of Gilgamesh's selfish and arrogant ways. For most of his life before he meets Gilgamesh, he has been kept away from people, living in the wilderness, and therefore hasn't had the chance to become wicked or selfish like other people.
From his relationship with Enkidu, we see some of Gilgamesh's weaknesses disappear and become replaced with strengths. Throughout his journey, we see Gilgamesh demonstrate strength in the form of literal physical strength, but a loving friendship teaches Gilgamesh compassion and empathy, and Enkidu's death causes him to work to eventually accept the fact that he is mortal. Over the course of his friendship with Enkidu, we see Gilgamesh's transformation from a demigod terrible to behold to a man with limitations, just like anyone else.