Also a real live phrase "to have the luck of the devil" or "the devil's own luck"?
In any case, it means that a person has an unnatural amount of luck. One could say that, because the DO isn't bound by the Pattern, he creates his own luck.

It's interesting that RJ indicated that Mat's luck is in a way related to the DO's own luck (might be a candidate for the little, important detail):

Question: "In The Dragon Reborn, Lanfear visits Mat as he is recuperating from his One Power surgery over the dagger. At one point she stretches out her hand towards him and he feels a tingle going over him, somebody interrupts them, and she turns her head and sobs, at about the same time a member of Black Ajah stole angreal and ter'angreal [only ter'angreal, actually - Terez] out of the Tower cache, one of which was a ter'angreal that was known to have some effect on chance. So it was about this time that Mat's really really really weird luck and the dice rolling in his head began. Is this a connection or coincidence?"
Jordan: "That is a coincidence. When they say that Mat has the Dark One's own luck, he can get as mad as he wants to, but in a way it is true. It wasn't a gift from Lanfear, though."
Question Part 2: "In that case, what was Lanfear doing?"
Jordan: "She was checking his health. She doesn't care very much, except that he is important to Rand, to Lews Therin, him and Perrin both, so she is interested in, the one she wants mainly is Lews Therin, or wanted anyway, and uh, so she is interested in these other two ta'veren, who seemed to be tied in with him, because they might be important to him."