Straight, True, and Clear
Spellbound's eager to give you symbols and explain them all. In fact, in a major way, this movie's mystery is all about the analysis of symbols. (Which is a huge reason that us semiotics nuts at Shmoop watch Spellbound every time it starts snowing.)
The theremin-music-inducing parallel lines are a big example—Ballantyne freaks out whenever he sees black parallel lines on white. When Constance makes marks with her fork on a tablecloth, he gets all cranky and upset. When he sees lines on her dress, he becomes distressed.
Parallel white lines: you wouldn't think you could be afraid of that, but Ballantyne manages it.
So what do those lines mean to Ballantyne? Does he have parallellineophobia? Nope.
Take it away, Constance:
CONSTANCE: Ski tracks in the snow. That's what those dark lines symbolize for him. His horror of them means, of course, that they are immediately connected with the cause of his amnesia.
"Of course," as Constance says. Edwardes was murdered on skis, and Ballantyne saw the murder. He developed a phobia of ski marks, along with amnesia. It all makes perfect sense… if you're writing a suspenseful Hollywood movie.
But these parallel lines symbolize more than just boring ol' ski tracks.
Wheels Within Wheels, Lines Within Lines
The parallel lines show you how the film uses symbols and how it thinks about symbols. Symbols, in the world of Spellbound, don't have much complexity—lines on a tablecloth = ski marks. The first is just a visual reminder of the second. It's a mystery because you don't know the connection between forks marks and skiing, but once you see the connection, there's an "aha!" moment.
In fact, you could argue that the parallel lines symbolize the clarity and simplicity of symbols in Spellbound. All this disturbing, weird imagery has a simple explanation. The title at the beginning of the film declares:
Once the complexes that have been disturbing the patient are uncovered and interpreted, the illness and confusion disappear… and the devils of unreason are driven from the human soul.
Figure out what the parallel lines are, and all is well. Yay.
A Bend in the Straight Lines
But you wouldn't actually expect Hitchcock to just give you a symbol and then give you an easy analysis of that symbol, would you? (Not if you're a Hitchcock fanatic, you wouldn't. The Master of Suspense is tricksier than a hobbit.)
So we've established that parallel lines are read as ski tracks. We've also established that those parallel lines can be symbolic of Spellbound's simplistic view of symbolism. But there's another, more complicated layer.
Those ski tracks, after all, ultimately symbolize death; they're the tracks that took Edwardes over the cliff.
So you can drive off those "devils of unreason" all you'd like, but you've still got a corpse left behind. We're going to go out on a limb (or an icy ski slope) and say that this extra layer of symbolism points to Mr. Hitchcock himself—in his movies, even when everything is neatly tied up and explained away, the body count is still unsettlingly high.