The answer is,
A good opening should promise the reader a powerful emotional impact if he or she reads on.
I'm convinced that people read stories primarily for emotional impact. If we wanted information, we'd be reading news magazines. If we wanted beautiful language, we'd go for poetry. If we wanted insight, we might be reading philosophical texts.
In fact, have you ever noticed that we don’t really have “genres?” We tend to buy fiction based upon the emotions that the books promise to arouse—romance, thrills, horror, wonder (in science-fiction and fantasy), justice in Westerns, and so on.
All readers, before they ever crack open a book, begin looking at a book hoping for clues as to what the big emotional payoff will be. Those clues can be found by where the book is placed in the racks on the store, what the cover image looks like, the title, and the author’s reputation.
Now, I can think of a number of ways to promise a powerful emotional experience.
Yet authors often fail to recognize what their readers’ needs are. I can't tell you how many thousands of times I've read stories for science fiction or fantasy contests that failed to arouse any sense of wonder at all. In the same way, I've seen horror stories that fail to arouse a chill, and dramas that were just plain dull, and comedies that were more grotesque than clever.
So how do you convince me as your reader to continue on?
Sometimes an author's sure use of prose is enough to convince me. If you write skillfully, if your descriptions are crisp and your characterization is sure-handed, I'll probably read on just because I know that I'm in the hands of a pro.
In other cases, the use of a great opening hook will do it, or perhaps the author's subtle use of foreshadowing.
Just as often, a compelling storyline will do the trick. If you quickly show an irresistible problem that confronts your characters, that will carry your reader a long way into your tale.
But the single most effective way to promise a powerful experience is to write an opening that in itself creates an emotional impact.
The first scene can be anything—a funny incident that introduces one of your protagonists, or perhaps an argument that leaves your reader shocked. Maybe you'll write a scene that will leave your reader admiring your protagonist and cheering for her, or perhaps you'll introduce your tale with a gruesome murder that will leave the reader horrified but burning with intrigue.
Whatever you do in your opening, a great opening scene will almost always find some way to arouse a powerful emotional response in the reader—and the impact of that scene will convince the reader to delve further into the tale, hoping for more.