The chapter starts out with a sick Zeezrom. He's not sick because he caught the swine flu or any other physical ailment; he's sick because of his mental and emotional anguish. Here you have one of the most wicked men of the day. He's convincing everyone in the village that there is no Christ; therefore, you don't have to repent. The reason for this claim wasn't because he believed it, but he was a lawyer and was seeking for money and power. He contends with Alma and Amulek and as a lawyer convinces many, but he ultimately is convinced by Alma and Amulek that he is wrong. Despite all of his efforts to reverse what he had said, the people ultimately throw Alma and Amulek in prison, beat them, burn all of the scriptures, and throw their followers in the fire while forcing Alma and Amulek to watch.
Zeezrom leaves the city with the full knowledge of what he has done. He also believes that Alma and Amulek have been killed. This is the cause of his sickness. He sees no way for to repay for what he has done. Then, he hears that it's only 99% as bad as he thought because Alma and Amulek are still alive and in the very city where he is staying. Then, he sends for them. Now imagine this. You've just had a heated argument with these two missionaries. You left them in the hands of a murderous people who treated them harsh. And you've been the cause of great agony to these two men of God. Yet, he sends for them because he knows they are men of God. That takes some guts.
The scriptures say that Alma and Amulek went to him immediately, obeying him. I think that takes some guts as well. If this had been me, I'd be more likely to say, "I hope he never recovers from his illness. Let him rot. Do you know what I just went through because of him-not to mention those poor people who were burned alive. (Amulek may be able to add, "I lost my wife and children because of him" just speculation though)." Instead of saying this, they simply obey his message and go to him immediately.
Then, comes these important words, "Believest thou the power of Christ unto salvation." Finally, Zeezrom answers in the affirmative. Alma tells him, "If thou believest in the redemption of Christ, thou canst be healed." And so it is that Zeezrom was healed both physically and spiritually.
Mormon proceeds to contrast Zeezrom to his followers. "But...the people of Amoniah did not believe in the repentance of their sins."