She is his “wife.” In effectively East Germany at the height of the cold war, where anyone could be suspected of being a spy (Loid is a spy), they rush a marriage for convenience. Loid gets a family, which makes him look less suspicious, and Yor is an assassin, so her reason is also to avoid suspicion. They’re not genuinely in a relationship, although in the anime they are kind of settling into the idea.

Edit: oh wait I’m like 40 minutes late to this there’s already another comment, oh well have another comment