Quiet and polite because you are shy. Also applies to clothing.
“I was more demure than a bonnet on Sunday morning.”
Note: usually applied to women, as in, 1950s females who’ve yet to sink their apathy in vodka. As in, “She was demure around the office, staying at her desk and smiling nicely whenever one of the men walked by.”
Though, it isn’t only applied to females:
“Trump’s demure wool attire with a cinched waist came from the age-old Parisian fashion house Christian Dior and riffed on its signature Bar Jacket.” —from APNews.com
Male or female, just don’t confuse demure with demur.