I heard this phrase on NPR tonight for the first time; googling it turns up its use, but not its meaning or origin. From what the nice man on NPR said, it sounds like it could mean some kind of protection from superstition or evil, but I could be way off base.
What does it mean? Where does it come from? Me, I’ve never whistled past a graveyard in my life, so far as I know. Or maybe I have…
As I’ve heard it used, it’s a way of expressing nervousness/fear. As one might do if one lived in a rural area and had to walk past a graveyard at night. I think it may be mentioned in Tom Sawyer or Huckleberry Finn.
I understood it to be similar to what Hamlet did as he dragged the corpse from his mother’s chamber. Whistlingin the dark, to keep your spirits up and put a brave face on things. If you are not afraid, the bogeyman cannot pounce on you. 
**Zabali ** did a better job of expressing what I was trying to say.
Oft in the lone church yard at night I’ve seen,
By glimpse of moonshine chequering thro’ the trees,
The school boy, with his satchel in his hand,
Whistling aloud to bear his courage up,
And lightly tripping o’er the long flat stones,
(With nettles skirted, and with moss o’ergrown,)
That tell in homely phrase who lie below.
Sudden he starts, and hears, or thinks he hears,
The sound of something purring at his heels;
Full fast he flies, and dare not look behind him,
'Till, out of breath, he overtakes his fellows,
Who gather round and wonder at the tale
Of horrid apparition tall and ghastly,
That walks at dead of night, or takes his stand
O’er some new-open’d grave; and (strange to tell!)
Evanishes at crowing of the cock.
– Robert Blair, 1743
Oh – That is an excerpt from The Grave.
I don’t know if the meanings of the phrases are identical, but there’s a German idiom about “whistling in the forest.” I’ve always understood as pretending to yourself to be courageous, although you aren’t. You’re full of fear, but in order to cover up this fear and detract from it, you whistle.
Also, whistling in the forest (or in the dark) serves a very definite practical purpose – it keeps the wild animals away!
While most of them do not hunt humans, they will attack if surprised or startled. And many species can severely injure a lone human. So whistling will make them aware of your presence, and they will move away, thus making your trip thru the dark forest safer. This was well known to the people living outside the cities in the past. Even today, hunters & hikers are well aware of it.