This summary is not the rule. The rule text controls.
When a judge appoints a lawyer to represent someone, the lawyer usually has to take the case. Lawyers can't just turn down an appointment because they don't want it or find it inconvenient. Courts rely on lawyers to step up and represent people who need help, including people who can't afford their own attorney.
There are only a few good reasons a lawyer can say no to an appointment. First, if taking the case would force the lawyer to break ethics rules or other laws, they can decline. Second, if the case would cost the lawyer too much money to handle properly, that counts as a valid reason too. Third, if the lawyer feels so strongly against the client or the case that it would hurt their ability to do a good job, they can ask to be excused.
This rule matters because it protects people who need legal help but can't easily get it on their own. It stops lawyers from picking and choosing only easy or popular cases while leaving harder cases unrepresented. At the same time, it recognizes that lawyers shouldn't be forced into situations where they'd be doing something illegal, going broke, or unable to represent someone fairly because of a serious personal conflict.