You know that one sappy story about his childhood that your uncle tells at every family gathering? The one about how ice cream was a quarter and he'd get a double scoop of strawberry before going fishing at the ol' water hole, because that's "what kids did in the days before Snapperchat and Instantpics"?
Well, Finch has this really maudlin memory about a dead bird. And he tells us about it approximately one million times over the course of the novel. Long story short, when Finch was a kid, a cardinal flew into a window in his living room over and over until, one day, it died. Finch, being Finch, held an elaborate funeral for it and has obsessed about the whole thing ever since.
Finch names this incident as the source of his "first black mood" (45.61) and he thinks about the cardinal whenever he's feeling down, which is often. At first, he felt guilty for not saving it. Over time, he's come to think of the cardinal's death as a suicide:
The cardinal was dead either way, whether he came inside or not. Maybe he knew it, and maybe that's why he decided to crash into the glass a little harder than normal that day. (25.9)
You may have noticed that Finch is also a bird name. That's not an accident, guys. The dead cardinal symbolizes Finch. When it died, Finch said, "There was nothing to make him last a long time" (45.60). He quotes himself on the wall of his bedroom before he commits suicide.