Story is driven by desire. But desire alone isn't enough to create engagement. Desire unchallenged isn't interesting. It's only when desire is met with conflict that things get interesting. Because it's only when there's push-back that there's uncertainty. And there's no element more important to engagement and drama than uncertainty.
A character has a desire. She comes up with a plan of action and sets out to pursue that desire. She is met with conflict and an uncertainty arises about whether she will attain her desire. But even here, our drama's still not engaging. Why? Because it doesn't matter. Another key ingredient to great drama is that there are consequences to both failure and success. In other words, something's on the line in the pursuit of a desire. Something's at stake. The outcome of the battle has an effect on the character's life. We call these consequences of outcome "stakes". Stakes make the win savory, and the loss bitter. Stakes make the drama matter.
There are great treasures upon her success, and wicked terrors upon her failure. There are consequences to the conflict. But that's still not enough. Indifference about a character's future nullifies the stakes. Why should we care about the consequences of this battle if we don't care what happens to this character? This is where empathy comes in. The audience must, in some way, have an interest in the future of this character, either through fascination, concern, admiration, or hate. With that interest in the character's future comes a deep concern with the consequences of the drama.
We've got desire, conflict, uncertainty, consequences, and empathy. There's a pursuit, a push-back, a consequence to the uncertain outcome, and we care that it's happening to this character. For our final ingredient of drama, we must force the outcome. Because even with uncertainty and consequences, the audience will lose interest if it appears that they'll never actually get a determination as to whether the character's desire was attained or subverted. If there's no end in sight, we lose interest. Who wants to play a game where the winner is never revealed? The final ingredient of drama is urgency. We must set an implicit or explicit deadline to the outcome so that a determination is made. These deadlines can consist of time constraints, option constraints, or an inevitable convergence of conflict (such as an approaching antagonist). Without some sort of urgency in the form of a perceived deadline, there's anticipation but no suspense. If there's no deadline, after all, the protagonist can just put off the outcome for as long as it suits her (especially if she feels like she's losing).
There's an implicit question raised in a dramatic situation, which we might call "the dramatic question." In short, it's "Will the protagonist attain her desire?" This question looms over the duration of the dramatic situation. "Will she? Won't she?" And it is this question that is the heart of suspense. Our eyes stay glued to the page, waiting to find out the answer to this simple, consequential question.
The elements of great drama are few and deceptively simple. And with that come a few words of caution, especially about "uncertainty" in drama. Uncertainty can be lost if either side of the conflict is too powerful. In other words, if your antagonist so incredibly outmatches your protagonist that there's not even a chance of success, or if there has thus far been no sign that the protagonist can win anything, then the audience may write off the protagonist completely and feel no uncertainty. This is one reason why sometimes you've got to let your protagonist actually win in order to allow suspense in the future. You must introduce hope to maintain uncertainty. On the other extreme, be sure your protagonist isn't overpowered. Nothing is more boring than a protagonist that plows through any hint of conflict with ease. The importance of a great antagonist cannot be overstated. As a general rule, add more danger to add more uncertainty.
With that, here are the ingredients of a compelling, engaging, suspenseful dramatic situation: desire, conflict (giving rise to uncertainty of outcome), consequences in the form of stakes, urgency in the form of a deadline, and empathy for the character. To heighten the suspense, increase the uncertainty, raise the stakes, and magnify the urgency. Suspense is fundamentally about asking a question to which the audience wants to know the answer—now.
You can also learn about dramatic irony as it relates to suspense here.