Once you've perfected the first chapter, it's important to follow up with an equally compelling, entertaining, and/or suspenseful second chapter.
If the first chapter is your hook to draw in readers, then the second is your opportunity to introduce the characters in greater depth. You've already shocked or intrigued your readers with the first chapter; use the second to explain who the characters are.
The danger, of course, is to launch into the backstory (if you managed to avoid it in the first chapter). This runs the risk of boring your readers into dropping the book and trying a different one.
Instead of describing your character with overwrought and weighty backstory, illustrate your character's background by showing how he or she deals with a situation.
For example, my current project "Paradise Found" opens with a fight scene where the main character is nearly killed for the identity chip in his arm.
In the second chapter, it's tempting to have paragraph upon paragraph of explanation. I'll provide a few examples. First, is how not to do it. The second (I hope) is better.
Warning... don't write your second chapter like this: Joseph Carrigan was an eighteen year veteran of the Chicago police force. He'd gotten his start in the anti-militia unit, followed by a three-year tour in anti-drugs. A short stint in IA later, Joe decided he would never hold a desk job again, much less one that had him looking sideways at other cops. So, he'd returned to the streets, and had been there ever since.
Try writing your second chapter like this instead: Joseph Carrigan stepped through the doors of his precinct, relieved to have survived his recent encounter with two muggers. A few years ago, he would have taken both of them without trouble. This time, he'd been lucky to receive only a goose egg on his head as a stern reminder of his slower reactions. While Joe was still enjoying the visual orchestration of chaotic movement of officers, detectives, witnesses, and detained persons, he saw one man moving with unusual purpose.
Even without the perfectly trimmed salt-and-pepper beard and insistence on wearing dress blues at all times, Joe would have recognized the man who was cutting through the crowd in his direction. Officers hurried to get out of his way, detectives decided to ask him their questions later, witnesses ignored him, and detained persons tried to avoid eye contact.
Not that it mattered, of course. The well-dressed cop focused his hard, gray gaze only on Carrigan. Somehow, Joe managed not to flinch or look away. Joe had known men more intimidating than Captain Stillwell, but the names of those men escaped him as the captain came to a stop in front of Joe.
"I knew there was a reason we shouldn't let senior investigators patrol alone," Captain Stillwell said, loud enough that some of the officers stopped typing their reports on their handheld computers, and a few of the detained persons glanced toward Joe, wondering if he was in as much trouble as they were.
"Captain," Joe tried to explain, "I wasn't on patrol yet. It was a simple mugging, and I'm--"
"What you were doing patrolling before your shift, is beyond me," the captain continued, disregarding Joe's claims of being an innocent pre-shift crime victim.
"I'm fine," Joe groused, "not that you asked, sir."
"Well, why wouldn't you be?" Captain Stillwell demanded. "You're too stubborn to ride a desk like most cops with your experience, and--"
"The ID Theft Taskforce needs someone with my experience out on the streets, Captain," Joe argued impatiently. "Contrary to popular belief, you can't solve every case by staring at a computer screen!"
"And," Captain Stillwell overrode Joe's protest by speaking louder, "you're too proud to realize when you might need back-up. You're right about one thing, though. The task force does need you, so I'm assigning you a partner." The captain raised a hand, stopping Joe's exclamation before it found breath. "No argument, or I'll have you cataloging evidence until you retire."
Reluctantly, Joe shut his mouth, and his shoulders slumped. The captain didn't pull out the big threats like that unless he was serious. "Understood, sir. Who will I be patrolling with?"
Conclusion: The better option draws the reader into the conflict between the characters introduced in the second chapter. It also introduces the captain without going into backstory about where they met, whether they were partners, why they get on each others' last nerve, etc.
Here's a writing prompt. Try writing it in the second style. Include dialogue and just enough description to differentiate the characters. Remember, it doesn't have to be a fight scene to be exciting.
Writing Prompt: She just knew there was going to be trouble on the docks. If not today, then sometime this week. As she stepped past the pool of light provided by the guardhouse, she realized the trouble was about to start right here and now...
Have fun, and keep writing!