She is described as unusually tall, blonde, athletic, and "coldly beautiful." She tends to be eerily calm in stressful situations, scarily practical, and more paranoid than Marcone.
She is introduced in Death Masks, saves Harry from Li Xian in Dead Beat, was "on an assignment elsewhere" during White Night, plays a slightly larger role in Small Favor, helping with the rescue mission, and goes with Harry to see Vadderung in Changes.
She has, at various points in the series, used a sword and shield, a double-bladed axe, and an assault rifle. She knows how to fly a helicopter, and does so in both Death Masks and Small Favor.
Her status as a valkyrie makes her very resiliant, as witnessed by the fact that she's eviscerated in Small Favor, but manages to get well again very quickly. She is an immortal, in that she doesn't age, though presumably she can still die from fatal enough injuries. She's also a magic user, though her magic seems to be connected to old Norse runes, and she appears to be especially proficient at wards and defensive-type spells. As a Chooser of The Slain, she has the innate ability to know when people are going to die, though this is not set in stone as the future is always changing (however, according to her, "there will be consequences").
Throughout a series, there's a hinted romantic relationship between she and Hendricks.
"Sigrun" is arguably one of the best-known valkyries in Norse Mythology, and a major character in the saga of Helgi Hundingsbane, found in the Poetic Edda. It's unknown whether she's the same figure or not.
In Heorot, Gard reveals that she's the scion of the Geats; presumably of Beowulf himself.