One of the classic motifs of comic book collections was "Secret Origins", where you could basically slap any disparate group of reprints together, and as long as they were origin stories you had a theme! I don't know who first thought of adding the word "Secret" to the concept of the Origin story, but it helped make the reader feel like they were getting inside information, which is always exciting.
For the first time, a DC digest book features a new story, this being "The Secret Spell!" by Gerry Conway, Romeo Tanghal, and Vince Colletta, which is the origin of Zatanna and Zatara. I think it's a safe beat this was an inventory story lying around and DC thought why not put it in a digest? Zatanna had a brief solo run in Adventure Comics, maybe this was originally intended for that.
The other Secret Origins are:
"The Origin of the Justice League" by Gardner Fox, Mike Sekowsky, and Bernard Sachs (a classic!)
The Demon in "Unleash The One Who Waits" by Jack Kirby (definitely an off-beat choice!)
"Earth's First Green Lantern" by Fox, Gil Kane, and Murphy Anderson
Deadman in "Who Has Been Lying In My Grave?" by the late, great Arnold Drake, Carmine Infantino, and George Roussos
"The Origin of Wonder Girl" by Marv Wolfman and the unusual art team of Gil Kane and Nick Cardy
...along with a text-piece all about the Zatanna origin and the storyline starring her that ran across several titles in the mid-60s, culminating in Justice League of America #51.
You can see by running Demon, Deadman, and Zatanna tales, there was a definite mystical bent to this collection. Maybe DC thought they couldn't sell it without the bigger name superheroes in there as well, but it might've been neat if they had added Swamp Thing, The Phantom Stranger*, or The Spectre origin stories to have an all-supernatural collection.
*Though of course, The Phantom Stranger has never had a "Secret Origin."