This explanation holds for the year that Snape was actually appointed DADA Professor. Why he wanted the post before then is explained further down.
The summer before his appointment as Defence Against the Dark Arts teacher Snape discovered that the current Headmaster, Albus Dumbledore, had only a year to live.
So, taken together, Snape would have known about the curse. It didn't faze him, though. He knew that he had a good shot of becoming Headmaster under Voldemort if he played his cards right. Even if Dumbledore were to confound his diagnosis and live for more than a year the curse need not bother Snape. He can leave Hogwarts and become a full-time Death Eater (and spy).
What about all the previous years when Snape still wanted the job?
It's true that Snape wanted the job, even before he knew that he might go on to become Headmaster. If Snape knew about the curse and had no clear idea what he would do after the DADA job, why would Snape still seek after the position?
Presumably, he assumed that he would be able to stay at Hogwarts. He can simply go back to teaching Potions come the end of the year. FailingWe know that, he can leaveliked it at Hogwarts and become a fullthat he enjoyed the comfort and safety of the castle. And, despite his obsession with Defence Against the Dark Arts, he obviously also loves Potions. He was an expert Potion-time Death Eater (and spy)maker with a decade of experience in the job. There's no reason why, if he'd hired a temporary or inferior Potions teacher, that Dumbledore wouldn't give Snape his old job back at the end of the year. Ron at least thought that that was what might end up happening.
"He might just go back to teaching Potions at the end of the year," Ron said reasonably. "That Slughorn bloke might not want to stay long-term, Moody didn't."
(Half-Blood Prince, Chapter 8, Snape Victorious).