Time flows differently in a story, and you can use the freedom from real clocks and calendars to set your story free.
Most obviously, you can manipulate time and the reader experience by the use of flashbacks and flashforewards and parallel storytelling and fracturing. Many stories raise question that, if the story were told chronologically, would already be answered -- but withholding information is part of the fun of stories, leading to emotional payoffs as surely as putting a joke's punchline at the end. Secrets always add to fun.
On the opposite side, reordering important reveals, such as the death of the main character in Sunset Boulevard, expectations are set (so the audience does not expect a happy ending) and dread is increased.
A third reason for this kind of time is to assure rising conflict. The logic of a story may not take the protagonist along the path of worse and worse complications, but manipulating the order of scenes (and the protagonist's awareness of what has happened) can up the tension and avoid dramatic plateauing. Oedipus has murdered his father and married his mother long before he realizes his mistakes, long before they transform his story.
These composition choices don't match real time, but, unless the writer messes up, all of these approaches are apparent to readers. In fact, they usually are called out specifically by starting new chapters or, at least, sectioning with added white space.
There are less obvious choices. Compression (where we don't see every moment of a scene) happens in film so often, we probably don't notice it. (Those who first saw movies did notice.) It can be used in novels and short stories, too. Actions described are limited to those that are essential without destroying flow. Summation is used to present scenes that are needed for logic but don't have enough interesting going on to offer moment-to-moment.
Obsession represents another use of time. Real people are regularly distracted by and drawn away from their pursuits of even critical goals. We all need to deal with eating, sleeping, phone calls, headaches, itches, and wandering minds. These are limited in stories to the point of what would be syndromes or diseases for any of us. Protagonists, on the other hand, are monomaniacal about their goals. If they were real, we'd lock them up.
One way obsessions are hidden is through timeboxing. We all understand deadlines, and the ticking clocks in stories feel right for us and automatically add tension that both increases our enjoyment and keeps us from looking too closely at the artifice.
Everything can't have a deadline, or course. That can become tedious or exhausting. Usually, the big event has a deadline. Rocky has both a deadline for the beginning of the fight (when training ends) and the fight itself (with the limited number of rounds). There may be deadlines for some of the tasks that must be accomplished to succeed, but probably not all.
Deadlines for tasks can be flexible or end in failure, provided alternative task that make it possible to stay on the road to success are hinted at. The final deadline almost always must be firm, or readers will feel cheated. Villains can have deadlines, and these can turn out to be flexible if it messes up the protagonist. Supporting characters can have deadlines for subplots or that make the protagonist more miserable.
Irreversibility is another subtle use of time. The idea that a choice made provides no way for the protagonist to go back and resume his or her original life is essential to story drama. Time branches, and the road not taken can never be taken. Decisions matter. They have consequences. And the one-way nature of time enforces this.
Finally, there is subjective time. We feel this in our own lives, when things seem to speed up (often during a crisis) or slow down (when life gets dull). Controlling the expression of this in stories is one of the writer's most important jobs. Getting it right is intrinsically linked to pacing (something I covered in the Fast Reads series).
Time is stories is a mixture of emulating time in our own lives and choosing techniques we can master to manipulate tension, surprise, and emotion within a story. The many approaches are your toolbox as a writer to make your stories more engaging. It's good to experiment with using these tools so you can create the effects you want. One caution is to be careful about using them in ham-handed fashions that take readers out of stories. Pay attention when you notice in your reading that other writers have not succeeded. These are great lessons. (And, since readers change, you can often find what would be failures today in "classic" novels from earlier eras.)
When the use of time does not feel authentic, it's like seeing the wires used for improbable leaps in Hollywood action scenes. Get good at this. Readers are more and more likely to spot techniques with time, so special attention (often during revision) needs to be paid to hiding you tracks.