Essentially, it’s saying to give your reader something interesting right from the start—do not bore your audience. This doesn’t mean that you have to start in the middle of an action scene, though that may do the trick. Begin your story with something entertaining that will cause your reader to want to continue reading.
In days past, writers could get away with a more leisurely introduction. One of the most common complaints in both The Hobbit and Lord of the Rings, for instance, is that the first chapter is so tedious that it’s hard to get past, but once you get deeper into the book, the stories really take hold. We don’t have that luxury now as your average reader doesn’t have the patience nor the time to spend wading through material that is uninteresting.
As for that previously-mentioned “hook”, that is merely what sets your story apart from others. Why should people pick up your book instead of the next on the shelf? Is yours doing something unique or going in a direction unexpected for its genre? You can also think of the hook as the inciting incident, that one event that kicks off your story. The inciting incident can literally be anything, but the more interesting and exciting it is, the more your audience will want to continue reading.
Think of the opening of Jaws (the book or the movie). The young woman runs out into the ocean to go skinny dipping only to be attacked by a shark and killed. It’s shocking and unforgettable. It also sets the story in motion. So it servers two purposes—to establish the tone and events of the story, and to capture the attention of the audience so they will continue with the story.
Your opening sentence goes a long way to accomplish this (“It was the best of times, it was the worst of time” and so forth), but also think in terms of entertainment value. Will describing the weather excite your reader (“It was a dark and stormy night”)? Will long explanations of your characters’ back stories make your reader care about continuing on?
Pixar’s method of beginning a story is to show your protagonist doing what he loves most, and then pull the rug out from under him. Obviously, in the Jaws example, the opening scene doesn’t show the story’s hero, Chief Brody—but the next scene (at least in the movie) does. We’re introduced to him waking up in his nice home he recently relocated to with his wife and kids and he gets a call from the office. He’s shown in his safe comfort zone, but the shark attack will shake all that up.
There are many wrong ways of starting a story, and often you’ll need to rewrite the opening to get it just right. And don’t forget that the beginning is just that—you’ll still need to craft a compelling and entertaining middle part that leads to a satisfying ending. However, put effort and thought into the best way to bring your audience into your story and compel them to want more.