While it may not necessarily be crucial for your readers to know the detailed life story of peripheral characters, having a set backstory for minor characters can help you as the writer know how to write those characters better.
Even if it’s not stated in the story, it’s good to know what makes your characters tick, including the ones that don’t seem all that imperative to the plot. If a character exists in a story, they should have a function. Knowing your characters is important because it’ll help you easily write their actions or reactions to certain events without making them flat or uninteresting.
Give them a family. How many siblings do they have? Do they have pets? Are their parents around? If so, what’s the character’s relationship with them like? If they’re not around, why not? Do they have children or otherwise perform a caretaker role? If they don’t have any family around, that’s a good talking point. What happened? Was it by choice or force? Protagonists tend to let the readers know what their relationship with their family is, if they have one, and minor characters can have the same types of family-related drama that the protagonists have. Just because they aren’t the primary focus of the story doesn’t mean they shouldn’t have a story to tell.
Give them an identity and a style. What kind of clothes do they wear? How do they do their hair? What kind of music do they listen to? What is their favorite food? When is their birthday? What’s their favorite holiday and why? Do they have a job? If so, where do they work? If not, what do they do with their free time? Is there anything they absolutely love or vehemently hate? What are they and why does the character feel that way about those things?
Give them emotion and a personality. Do they get angry easily? Are they loud or quiet? Their emotions will stem from their past, so it’s important for you to have an idea of that, also. Do they speak their mind or keep their opinions to themselves most of the time? Are they a figure of trust for the main character(s)? Why or why not? There has to be some depth to them in order to make them convincing and just as much a character as any other in the story.
Of course, these are definitely things to think about for major characters as well, but a lot of writers can forget to give minor characters their own personal story, even if they never get a moment in the story’s spotlight. Minor characters are characters too, you know, and they deserve some thought.