Our main characters, the folks who are in charge of the story, have elaborate backgrounds that we bring out in various ways. They are described as they move through the pages, and we learn about relatives and friends, places they've studied, jobs they held, all sorts of interesting facts as the story calls for them. We insert a lot of this "backstory" in small doses to avoid slowing the pace.
But what about secondary characters? They can be just as crucial to the story, depending on the roles they play. So how much background should they have? I don't have rules for writing. That sounds too inflexible. But I have a modus operandi, to use a good crime-speak term, that I follow with below-the-top-tier characters.
a. Use some sort of physical description, not necessarily any of the usual height, weight, eye or hair color. Here's one I used for lawyer Arnie Bailey in the first Sid Chance book: "Bailey launched his short, chubby body through the door like a well-dressed groundhog storming out of hibernation."
b. Provide some background pertinent to the story. In A Sporting Murder, which involves a basketball franchise, I used this bit for Greg McKenzie's friend, Sam Gannon: "He grew up in a rural area south of Tulsa and met Wilma at the University of Oklahoma, where he played basketball."
c. Describe their relationship with one of the main characters. Sam Gannon's wife, Wilma, is the best friend of Greg McKenzie's wife, Jill. Here's a spot where I gave a little comparison of the two women: "The daughter of one-time missionaries to China, Wilma liked to say Jill was born with a silver spoon in her mouth while she arrived with wooden chopsticks."
d. If possible, show how they think, how their opinions differ or mirror those of the protagonists. Here's an example from The Surest Poison, where Sid reflects on his friend Patrol Sgt. Wick Stanley: "Without a feature unique enough to stand out in a crowd, he would have made a great undercover man, Sid thought. Wick had no interest in detective work, though. He liked to be out on the street, dealing with the rough and tumble of everyday life."
Walk-on characters who fill minor roles in the story need less description. When Greg goes to a delivery service to find out who sent him a bottle of Scotch laced with arsenic, I described the man he talked to this way: "An older man with an abundant white beard that made him resemble a character out of a nursery rhyme greeted us from behind the counter." The man, who had only three lines of dialogue, was described otherwise as squinting through large, round glasses.
As I said, these should not be taken as rules, just the way one mystery writer does the job. Other opinions may differ.