To "illuminate a conflict" means to explain a situation where there is an intense disagreement or clash of values. Teachers use the term to ensure that students can fully detail where a conflict is present in a text.
In analyzing texts, "illuminate" means to "bring light to something" or explore in a revealing way. Since you have identified The Catcher in the Rye as a subject, we can illuminate some conflicts here. One conflict exists between Holden and society. To explore this conflict, you would have to find evidence where Holden speaks about what he dislikes regarding the social setting around him. You might want to use his ideas about "phonies" to help you here as you illuminate this conflict.
Another conflict that can be explored is the conflict he feels within himself. There are many moments where Holden struggles internally with what he wants. In illuminating this conflict, I think that you can talk about how Holden talks about his age and maturity and his struggles in how he behaves: "I was sixteen then, and I'm seventeen now, and sometimes I act like I'm around thirteen." Exploring this conflict means you would talk about how what he says and what he does might be two different things.