When my agent accepts to represent one of my books - or movie scripts - she asks me to deliver a snappy summary of the plot and characters. This is also called a "pitch".
How to pitch HAMLET: "They killed his father - now he's out for revenge! Who will be the last man standing?" (A pretty accurate plot summary.)
However: A snappy plot summary is NOT the same as a synopsis. If you want to write a full (and successful) novel, begin with the synopsis.
A writer's own private book synopsis needs to be very detailed. It can - and often should- provide the "back story" and information the writer needs to "make sense" of his imaginary world. (Neither the reader nor the editor need to see the writer's synopsis. The version they get to see is more like a pitch.)
I go so far as to draw sketches of the characters and locations in a book. (Of course, if the location also exists in the real world, you can look it up. For instance, you can find a variety of detailed maps of every country in the world.)
If there is a major inconsistency or plot-hole in the story I wish to tell, it's always better if it shows up in my synopsis and preparatory notes... so I can work it out in advance... instead of appearing much later, after the book is released, when the publisher asks me to write a sequel.
Almost no writer escapes making an error now and then. Luckily, readers are a forgiving lot... but watch your step! Legend has it that Frank Herbert was mercilessly taunted by nitpicky readers. They would sneak up on him during conventions and say "Oxygen!" (Meaning: where does the oxygen atmosphere on the plantless, waterless desert planet Arrakis in Dune come from?)
The readers and publishers wanted sequels to Dune (and did they get sequels)... so Herbert had to work out the oxygen issue in later books.
When I wrote Terra Hexa, I took a huge leave of my senses. (Or two. Or three...) Instead of working out in advance how the imaginary world of the story actually worked and where it came from, I decided to not give a damn. I was convinced the book would never be published in my home country anyway... and a sequel to that book was as likely as a flying pig... so who cares? Wheeee!!
But such was the whim of a capricious fate, that it tossed a giant-size humble pie in my face. The publisher asked me to write a sequel. I'm writing it now. And I have to work out the issues I ignored when I prepared the first book... and the readers and critics have been kind enough to point out all the loose ends and inconsistencies.
It's nice to know they care. :)