Literally, "sanpaku-gan" (三白眼) translates to "three whites eyes". It refers to how the human eye can be divided up (see above for examples). As website Tofugu points out, sanpaku is when you can see three whites: one both sides and one either above or below the iris.
In his 1965 work You Are All Sanpaku, Ohsawa explained the concept:
In a healthy newborn child, the lower edge of the iris-the sphere of color at the center of the eye-rests below the lower eyelid like a rising sun. The eye has two white areas on either side of the iris. In the eyes of a dead man, the iris turns up into the skull. If it is visible at all it has three white sides. Sanpaku. As a man becomes old or ill, as he approaches death-whether he be seven years old or seventy-the colored portion of the eye-the iris-rises to disclose white between the lower lid and the iris.
Sanpaku, Ohsawa continued, would mean that something in the person's entire being was out of balance. Being out of balance meant the individual was, according to the author, "sick, unhappy, insane, what the West has come to call 'accident prone.'"
Continuing, Oshawa added, "The condition of sanpaku is a warning, a sign from nature, that one's life is threatened by an early and tragic end..." Oshawa pointed to individuals with sanpaku eyes that ranged from Martin Luther King Jr. to Abraham Lincoln—which, of course, implies that their untimely deaths had nothing to do with radicals upset about, oh, the Civil War or the Civil Rights Movement.
Oshawa's answer was a macrobiotic diet, which some individuals might find healthy. But the leaps Oshawa made were pseudo-science. And by his rationale, people who followed that diet would be less likely to be sick, unhappy, or even "accident prone". Inadvertently or not, the whole thing trivializes these well-known people's lives—and their deaths. And by Oshawa's logic, John Lennon, who ate a macrobiotic diet and even mentioned sanpaku on his Mind Games album, should never have been "accident prone".
"In the eyes of a dead man, the iris turns up into the skull."
But let's say you buy into this superstition: If you have a white above your iris, that means that you are possibly a danger to the outside world and unable to control your emotions. If you have a white below your iris, that means the outside world could be a danger to you.
If you do have sanpaku eyes, don't take much stock in these superstitions. As with most superstitions, this isn't hard science. It's not even soft science!
The other issue is what exactly sanpaku means, if anything, in its native Japan. Because while a Japanese writer helped popularize the notion of sanpaku eyes in the West, it doesn't seem to be much of a superstition in Japan—especially compared to other Japanese superstitions, such as people's blood types. There is a notion, however, that people with sanpaku eyes are apparently likely to commit crimes or are insane. That, or they're simply pissed off (which is how sanpaku eyes pop up in anime). And, yes, there are even those who say sanpaku eyes are "cute".