Give readers a reason to care and they'll read on. Problem is, sometimes you can have all the right pieces of good storytelling in place and the reader still doesn't care, but you're not sure why. This often equates to the dreaded "it was well written, but it just didn't grab me" type comments and rejections.
So how do you get those pesky readers to care in the first place?
"Go to bed" doesn't get much of a response. "Go to bed or else" does, because the "or else" could be something bad. The fear of that something bad forces a reaction. When the reaction you want is fear and worry (which leads to caring), you have to dangle something bad as a threat.
Let's say you have a scene where Joey is sitting at the dinner table, and his babysitter is forcing him to eat his broccoli. He refuses, she insists. This is going to get ugly and one person is going to end the night unhappy. Even though they both have strong goals to drive the scene, do you care if Joey eats his vegetables? Probably not. It doesn't matter if he does. Nothing will happen to him if he doesn't.
But let's say Joey is highly allergic to broccoli. He tells the babysitter, but she doesn't believe him. Joey knows if he eats that broccoli, he's going to wind up in the hospital. Heck, maybe he has some weird anaphylactic reaction and it could even kill him. And the babysitter is not above holding him down and shoving it down his throat. She's a lot bigger than poor little Joey, and she's known throughout the neighborhood for being the meanest babysitter in town. The chances of Joey avoiding that broccoli are slim. Curious what happens now? Probably, because the stakes are much higher now. Eating his vegetables has real consequences that matter on a large scale.
Not everything has to be life or death stakes, but if the outcome doesn't matter to the person it's happening to, why should it matter to anyone else? But if the outcome has dire consequences, we'll read on to see what happens.
To care, we have to worry about (or wonder) how things will turn out. To worry, the outcome has to matter in ways that will strongly affect someone -- preferably the protagonist or someone important to the protagonist.
Common Caring Failures: Low stakes dressed up to appear high. The protagonist feels it's life and death, but it really isn't, and the stakes end up looking melodramatic. Another one is having the stakes too high. Saving the universe is so huge that it becomes impersonal. It's hard to care about billions. It's too abstract.
2. Likable Characters
Even the highest stakes won't matter if readers don't like your character. The worry comes from them not wanting to see bad things happen to this person (even though we love it when bad things do happen to them). Readers like to see the struggle, to know the win was earned. And they want to know the person winning is worthy of the victory.
This also has a flip side. If readers don't like a character but are intrigued by them, they'll read to see what they do or if they get their just desserts. This is a lot more challenging however.
Common Caring Failures: Perfect characters who have no flaws and do everything right. Overly flawed characters who do everything wrong. Characters that have no redeeming qualities at all.
So now we have someone we like, who faces something bad happening to them if they fail. But you also need...
3. An Interesting Situation
The nicest guy in the worst trouble won't hold attention long if the problem is boring. What's worse, readers are inundated with so many stories every day, that even exciting problems can be boring if readers have read/seen/heard of them too many times. They can predict how the story will play out.
Common Caring Failures: Offering the same old same old. While you can make an old idea fresh, similar ideas done in similar ways rarely hold attention. Another common failure are situations that the writer find really cool, but their characters are just there to act out that cool idea. There's no story.
Create a situation readers haven't seen before (or a new twist on things they have), give them a character they like, and give them terrible consequences if they fail, and you'll have readers caring about what happens next. That is, as long as...
4. The Protagonist Cares
This is where a lot of "why should I care?" stories fail. They have the first three down, but their protagonist never worries that much, or stresses over the situation. Readers get their clues from the protagonist, and if that protagonist isn't that worried about something, readers won't be either. But if the protagonist is all wigged out, the reader will be too -- even if they know the situation isn't as dire as the protagonist thinks. The worry -- the caring -- comes from knowing the protagonist is worried and not knowing what they might do about it.
A protagonist who always wins, never struggles, knows he'll come out on top no matter what he faces, is about as boring as you can get. There's a reason they gave Superman Kryptonite. It's not really about watching someone win. It's more about watching them trying not to lose.
Common Caring Failures: Forgetting the emotional component to a story. Stories are more than just what happens, they're about how people deal with it.
To get readers to care, give them things to care about.