In Norse mythology, Sigyn is Loki, the trickster god's wife. Very little is known about her, and she's referred to only in a handful of paragraphs.

According to the stories, Sigyn is loyal to her husband even after his punishment for the death of Balder, where he was chained between some large boulders and a poisonous snake was placed over his head. Sigyn stays beside him holding a bowl over him to catch the poison. When the bowl is full, however, she has to leave his side to go empty it. When the poison drips in Loki's face he writhes in pain, causing the Earth to tremble.

Sigyn is sometimes referred to as Sygin or Syngin.

In the Elder Edda, Sigyn apprears in the following paragraphs, the first taken from Volsupa:

    "She saw a captive lying under the grove of hot springs,
    That evil-loving form, Loki she recognised;
    There sits Sigyn, not at all happy
    about her husband - do you understand yet, or what more?"
..and in Lokasenna:
    "He (Loki) was bound with the guts of his son Nari. But his son Narfi changed into a wolf. Skadi took a poisonous snake and fastened it over Loki's face; poison dripped down from it. Sigyn, Loki's wife, sat there and held a basin under the poison. But when the basin was full, she carried the poison out... "
..and in a longer passage in the Gylfaginning in the Younger Edda:
    "Then Loki's sons Vali and Nari or Narfi were fetched. The Aesir turned Vali into a wolf and he tore his brother Narfi to pieces. Then the Aesir took his guts and bound Loki with them across the three stones - one under his shoulders, one under his loins, the third under the backs of his knees - and these bonds turned to iron. Then Skadi got a poisonous snake and fixed it up over him so that the poison would drip from the snake into his face. But his wife Sigyn stands next to him holding a basin under the drops of poison. And when the basin is full she goes and pours away the poison..."

Sources: Various, most notably http://loki.ragnarokr.com/
Translations from the Elder Edda by Larrington
Translations from the Younger Edda by Faulkes