TL;DR: he was part of the "idealised father figure" theme in the series inspired by Rowling's poor relationship with her own father.
The only official word I've been able to find is the following, from an interview in which JK Rowling talked about various ways her own life and background influenced her writing in the HP books.
Rowling delved into writing at an early age, but her thoughts about love, death, heaven and hell were tested when her mother was diagnosed with multiple sclerosis in 1980.
"She had a very virulent form of the illness and at that time there were no drug treatments at all," Rowling said. "And they said 'well you've got multiple sclerosis, see you.'"
The illness devastated Rowling and her sister, and strained her relationship with her father.
"I was very frightened of my father for a very long time," she said in the 2006 interview. "...I also tried desperately to get his approval and make him happy, I suppose, and then there came a point quite shamingly late in life where I couldn't do that anymore, and so, I haven't had any contact with my father now for a few years."
Rowling's far from ideal relationship with her father inspired idealized father figures, like Hagrid, Dumbledore, and Sirius Black, in the series. She says the absence of any meaningful relationship with her father and the loss of her mother have been the two of the most important influences on her writing.
"I had been writing for six months before she died and, the weird thing is, the essential plot didn't change after my mother died, but everything deepened and darkened," Rowling said. "Harry was always going to lose his parents. And it was always going to be a quest really to avenge them, but to avenge everyone against this, this creature -- this being who believes that he can make himself immortal by killing other people. So that's, that that's something I'd created before she died, but yes, its seeped into every part of the books. I think, in retrospect now I've finished I see just how much it informed everything."
The only other piece of information Rowling has given out about Sirius in post-book interviews is his birthday, 3 November, which she promised to tell fans if enough of them supported her favourite football team - they did, so she made up a date for them. True story.