This is a very common question among new writers, or authors new to the age of digital books: "But What If Someone Steals My Work?!"
Actually, this fear can be divided into two parts. The first is the concern about one's ideas being stolen, up to the point that newbie authors discuss their plot twists with a cautiousness and secrecy that wouldn't have shamed KGB, and are reluctant to show their work to anyone else. Here is where I say: humility, humility, humility.
Let's put it this way: writers are a narcissistic bunch (saying this to emphasize a point, yes?). The ideas each writer admires most are... that's right, their own. So while your idea for a novel about dolphins with confused sexual identity might seem like a genius and an instant bestseller to you, another writer will probably roll their eyes at it and stick to their idea of a post-apocalyptic epic about deranged penguins attacking the McMurdo Antarctic research station.
Bottom line: writers have plenty of ideas, probably more than they can use in a lifetime. Mine are always flitting around like crazy bats in the light of a lone streetlamp. I can catch a dozen with a lazy sweep of a net. It makes little difference, as an idea is nothing without good writing and months, possibly years, of diligent work on a manuscript.
Another fear, perhaps a little more valid one, is the concern about book piracy. I just had a discussion about this not long ago with a writer to whom I suggested uploading her books to Kindle (she has dealt in print books exclusively until now). Her concern was, "but... but... this is a digital file!! People may pass it on and spread it around, and there will be nothing I can do about it!". My reply was, "yes, but if you don't go digital, you are missing on a whole massive chunk of market!!" Does it make sense to give up on the entire world of digital publishing out of concern that some unscrupulous people might spread your book illegitimately?
Book piracy is a rotten thing, and it can be a real concern. There are some laws against it, too, though enforcement might not be very effective. But... once again, humility. I can testify, for instance, that I ran a Google search, and nobody is stealing and spreading my books. I kind of wish they were, sometimes. It would be a bit of free publicity.
Decent people still buy books, and even indecent people are sometimes too lazy to seek out a pirate copy of a book, and the more you put your work out there, in as many formats as possible - print, digital, audio - the higher is your chance to get noticed (and earn money). Visibility, not plagiarism or book piracy, is the big challenge for a new author. Just try it and see for yourself.