Most of the events in the story help Ponyboy mature in some way. The story takes place over a relatively short period of time, so the book reads more like a single major event vs. a long period of maturation. I do think that a few sequences show punctuated development in Ponyboy though. There is no particular order to my list.
I think one event that shows maturity is the church fire. The entire goal of staying at the church was to stay low and off of the radar. Pony and Johnny were successful at that, and had the chance to leave with nobody knowing that they were there. The fact that Ponyboy ran back to the church to help the children shows that Ponyboy isn't focused solely on himself or the members of his gang. It also shows him taking responsibility for his actions instead of running away from them.
"I'll get them, don't worry!" I started at a dead run for the church, and the man caught my arm. "I'll get them. You kids stay out!" I jerked loose and ran on. All I could think was: We started it. We started it. We started it!"
A second event is at the hospital after the church fire. Johnny is hurt and in the hospital. Darry shows up at the hospital and expresses deep relief that Johnny and Pony are both alive. Previously Ponyboy thought that Darry didn't care for him that much. But the hospital scene showed Ponyboy that he had been wrong about his older brother.
In that second what Soda and Dally and Two-Bit had been trying to tell me came through. Darry did care about me, maybe as much as he cared about Soda, and because he cared he was trying too hard to make something of me.
The third event is from chapter 2. Ponyboy had just finished telling Cherry about what happened to Johnny to make him so nervous all of the time. Cherry responded to the story by telling Ponyboy that not all Socs are evil jerks. Ponyboy isn't so sure, but then Cherry says this line:
I'll tell you something, Ponyboy, and it may come as a surprise. We have troubles you've never even heard of. You want to know something?" She looked me straight in the eye. "Things are rough all over."
And Ponyboy believes her, and the reader believes Ponyboy. The sequence shows maturity in Ponyboy, because it shows that he can be empathetic to someone outside of his Greaser gang.