When Loki was young, he came to desire a wife, and admired Sigyn from afar. When he went to court her, she revealed that she was betrothed to Theoric. Loki arranged to have Theoric murdered but made it look like he was killed in battle, and then disguised himself as Theoric so that Sigyn and "Theoric" were eventually wed by Odin. At the end of the ceremony Loki revealed his true form. Odin was furious, but Sigyn noted that as his wife, she was duty-bound to Loki for life. Odin made her the Goddess of fidelity for her endurance, and banished Loki from Asgard.
Does this mean that Loki will be/have been married to Sigyn in the movie? We'll find out. But one thing is for sure: they all have the same taste in headgear. (Reindeer Games, Tie-Fighter, and Charlie Brown Christmas tree.)