To be a nosy parker is to look into other people’s business when you don’t need to, to be a busybody, or a snoop. It is mainly used outside of the United States, so much so that it has a variant spelling inside the US, nosey Parker. It does not need to be hyphenated unless used as an adjective.
The origin of the idiom is unknown, though some ascribe it to a postcard which referred to a peeping tom in Hyde Park. Parkers were park-keepers, but there is little evidence that the idiom was directly related to someone who worked for the park and spied on people.
Examples
I might like to know what’s going on… it’s my profession to be a nosy parker don’t you know… but when I do get told a story, I want everything, chapter and verse as there’s nothing worse than a half-baked tale. [Lancashire Evening Post]
Through the eyes of these women we see the thread of the story, a woman named Bettie Shelton. Bettie is a nosy parker, pesky, annoying-sort-of-neighbor who happens to be the founder of the Avalon Ladies Scrapbooking Society. [USA Today]
Hers is one of the houses open to nosey parkers for the Barfoot & Thompson Home and Garden Tour to raise money for the Starship Foundation. So, being a nosey parker, I wanted to go and have an advance look – at the house and the garden, and at her, because she has a formidable reputation. [The New Zealand Herald]