When Montag has the flashback to meeing Professor Faber for the first time, it is at a point in the novel when he has realized that he is incredibly unhappy, and he suspects that the answers to all of his questions can be found in books. He is forcing Mildred to read, and he is frustrated because he isn't understanding what the books mean to him. As he is sitting there, surrounded by his stolen books, trying to glean meaning from them, he remembers having met Faber at a park a year ago. He had seen Faber sneak something into his jacket, and when Montag approached, Faber had been afraid. But they had sat on a park bench and talked for a while. Faber had been self-assured, happy, and confident. That had really struck Montag at the time; Faber had even been bold enough to quote literature.
So, as Montag is searching for answers, in books, the only person he knows who seems to have loved books and understood them is Faber. Faber might have the answers. At the time he had met Faber, he hadn't thought anything of it, because he hadn't realized at that point that he was unhappy. But after Montag "wakes up" to his misery, he hopes that Faber can have some answers for him.
I hope that those thoughts helped; good luck!