She runs the bar in hell, so to speak. And, depending on what version you read, she may or may not give Gilgamesh some advice on what matters most in life.
Siduri is the tavern-keeper of the underworld. Where she comes from, and why she thinks running a tavern in the underworld is promising business opportunity, we have no idea.
We also don't know what her regular patrons are like down there; we would have figured the underworld would attract a pretty unusual customer base, but apparently Gilgamesh's haggard appearance when he shows up at Siduri's door spells bad news, and she immediately bars the entrance to him. That said, given that Gilgamesh immediately starts threatening to smash her door down, she clearly is pretty good at sizing people up. He then tells her all about his sadness at Enkidu's death and asks whether he will also die.
What happens next is interesting.
In the Standard Version (for more info on the different versions of the epic and how they matter to you as a reader, check out the "Writing Style" section of this module), Gilgamesh is really talking to himself—he doesn't wait for an answer from Siduri. He does ask her where to find Utanapishtim, and she tells him how to find Urshanabi, who will take him to Utanapishtim.
This Siduri? Not so exciting. We think her part would have ended up on the cutting room floor.
But in the Old Babylonian Version, after Gilgamesh explains the nature of his quest (and hence why he's so down-and-out looking), Siduri gives him a speech about how his quest is pointless, because the gods have forbidden human beings from achieving immortality.
Therefore, she says, Gilgamesh should spend his time enjoying the fine things in life: dancing, partying, decking himself out in sweet duds, and being a good family man: "Attend to the little one who holds onto your hand, let a wife delight in your embrace. This is the true task of mankind" (source 85).
As a further interesting little nugget, some translators interpret this last word as "womankind"—and take it to refer to a Sumerian cultural belief that intercourse was the natural duty of women. This does add some dimension to the whole scene with the temple-prostitute at the start (source 85).
What's cool about Siduri's words is that they start from the same insight as Gilgamesh's words to Enkidu in Tablet 2—we all die, and there's no escaping it—but they come to a different conclusion. Whereas Gilgamesh said the solution was to do great, dangerous deeds to earn an undying reputation, Siduri basically says, "Forget about that. Just enjoy a peaceful life while you've got it." Put this together with the last bit, and maybe—just maybe—the poem is suggesting that men and women are, you know, from Mars and Venus. Or something.
So, why would Sinleqqiunninni have left out all this in the Standard Version? We don't know. Maybe he didn't much like Siduri's advice. Maybe he got a cramp in his hand. Regardless of which version you read, Siduri's small part is still a major contribution to the story of Gilgamesh's search for wisdom. She also makes a concrete contribution by directing Gilgamesh to Urshanabi, the ferryman. When Gilgamesh leaves, it's the last time we see Siduri in the story.