I don't think there's any deeper meaning that just what it says: She's calling him an idiot. She's telling him that he doesn't know or understand nearly as much as he thinks about how the "real world" (her real world, at least) works.
Remember that, when the two met, Jon Snow had lived a relatively sheltered life. He grew up as a not-quite-noble, who was shuffled off to the Wall when he was just a teenager. I think he's supposed to be older on TV, but in the novels, he's 15. Once he gets to the Wall, he takes his vow of abstinence, and proceeds to be a Night's Watchman. That's the sum total of his real-world experience.
Ygritte, on the other hand, is a wildling who's has to survive, seemingly on her own, for many years. We never see any hint of parents, though as she's 18 when we meet her that may not be unusual. More importantly, she has clearly been in relationships before, and has learned how to take care of herself.
During their time together, Jon initially expects her to want to be treated the way the women he knows would, but his only source of comparison would be people like Sansa, or at best Arya. Ygritte is vastly different from them. Jon also exposes all of his prejudices about how the wildlings live, which Ygritte considers stupid. Jon is also clearly still a virgin, and when Ygritte starts flirting with him, his inexperience shows.
Initially, when she tells him he knows nothing, she means exactly that: "You think you know everything about my world, but you know nothing."
Later, after she warms up to him, the same phrase takes on more of a teasing tone. It's an insult, but a playful one, reminding him that she's the one with all the experience.