It gets hard for me to keep what is said in the books and what is said in the show separate, so the following is definitely in the books, not sure if in the show:
Winter is an event that reoccurs in westeros, but it's not seasonal. The summers a long, spanning years and sometimes even decades, but winter always comes.
Many, many years before the events of GOT, there was a great threat that almost ended the world. The assumption is that it was something like the apocalyptic threat we just witnessed in the last episode. Azor Ahai is the hero that prevented the end of the world of man.
Now, the big difference between the show and the book is that there is no night king in the books and I doubt that there ever will be, as I think the books will treat this more as almost a natural disaster than just setting up a big bad antagonist like the show went with.
I cannot remember if the show talked about previous battles against the Night or the winter, but I am pretty sure it did. How did those battles resolve without killing the night king? We saw how he was created. It doesn't make sense that the children of the forest would make another night king after the first one was stopped, so if the show did reference previous battles against winter, which I am positive that it has, (otherwise how do you explain the wall?) then how do they explain winning those battles without killing the night king?