Since the purpose of this exercise is to further develop your characters and plot, it could be anything that helps you achieve that goal. Here's what I wrote to another Prepper with a similar question, where I expounded on The Hobbit example:

Bilbo Baggins barely appears in The Lord of the Rings, but Bilbo's acquisition of the One Ring of it leads to Frodo's quest later. Another plot background story goes even farther back in time: the story of when Gollum, then named Smeagol, first acquired the ring. Other possible background stories: Sauron first forges the One Ring. Isuldur acquires the ring by cutting it from Sauron's hand. Sauron corrupts the wizard Saruman. Wormtongue corrupts Theoden. Aragorn's father, Arathorn, heir of Isuldur, is killed, and Aragon is placed in the care of the elves for safekeeping while Denethor ascends as steward of the throne. All these stories are critical to the story of Frodo's quest, and any one of them would be an appropriate background story that sets up the plot.

Basically, there are any number of events that happened before your story which led to your story. They could involve direct or indirect characters, settings, objects, cultures, anything. But it should be something new, something that you haven't thought about much - or enough - that will help you further solidify the story's background in your mind.

Regards,
Michelle