We all have things we have to do, whether we want to or not. When Bois-Guilbert loses the tournament match to Ivanhoe, we're pretty sure he doesn't want to hand over his armor and horse to this Saxon upstart – but he does it anyway, because those are the rules of being a knight. Likewise, when Prior Aymer and Bois-Guilbert arrive at Cedric's hall at Rotherwood, Cedric doesn't want to share his home with two Norman bullies – but he has to, because it's his duty as a lord and a host to be hospitable. These are both examples of clear duties that these guys carry out no matter how they may feel about them personally.
What if it's unclear where your duty lies, though? What about Ivanhoe, conflicted over his duty to his father and his duty to his king? Or Athelstane, torn between his duty as a subject of King Richard and his duty to his Saxon allies as a descendant of the Saxon royal family? And how about all those duties that people in this book just ignore, like Prince John's duty to his brother or King Richard's duty to his people? Duty is a powerful theme in the book because knights are supposed to care about it, but there's a huge difference between the ideal and the reality of duty in this novel.
While many of the characters in Ivanhoe, from Friar Tuck to King Richard I, acknowledge some sense of duty, very few of them follow through on it. While the ideal of duty is common throughout Ivanhoe, duty itself is not actually a strong motivator for action in the novel.
Because Ivanhoe portrays a medieval kingdom led by an individual man, King Richard's sense of duty (or lack thereof) has a major effect on the political and historical events of the novel. By portraying problems that arise when a king doesn't take his duties to his kingdom seriously, Ivanhoe criticizes any system of government that depends entirely on the emotions and character of one person.