Upon being resurrected at the beginning of Season 6, Jon Snow wanders straight into the arms of Ser Davos and Melisandre, who kindly throw him a blanket before peppering him with questions. We learn that Jon Snow saw nothing after dying on Game of Thrones, which is one of the first things Melisandre asks. The fact that he didn't go anywhere while dead actually clears up some fan theories and gives us an idea of where his character is headed.
In an interview with Entertainment Weekly, Kit Harrington gave fans some very valuable character insight (we are not worthy!) into how this fits Jon Snow's narrative. Namely, we are able to infer from his remarks that, since Jon Snow tells Melisandre he saw "nothing, there was nothing at all" between when he got stabbed in the heart and when he was resurrected, it means that Jon did not warg into his direwolf Ghost just before his body succumbed to death. Said Harrington:
"...That’s the most important line in the whole season for me. Jon’s never been afraid of death, and that’s made him a strong and honorable person. He realizes something about his life now: He has to live it, because that’s all there is. He’s been over the line and there’s nothing there. And that changes him. It literally puts the fear of god into him. He’s seen oblivion and that’s got to change somebody in the most fundamental way there is. He doesn’t want to die ever again. But if he does, he doesn’t want to be brought back."
And there's his other big reveal: that Jon Snow won't, as we've seen with Game of Thrones' other multiple-resurrectee Beric Dondarrion, allow Melisandre to perform her resurrection ritual on him a second, third, or fourth time, should he die again. This is actually a total blessing. Imagine how obnoxious it would be if we lived in a Game of Thrones universe in which Jon Snow's life never mattered because it could always be brought back.
On the bright side, we can also surmise that Jon Snow now has among the greatest motivations to stay alive of any figure in Westeros. He's known the nothingness of death, deeply, and will fight with all the survival instinct that knowledge drives to avoid dying again.