What does Ponyboy mean when he says "Johnny and I understood each other without saying anything"?
Ponyboy is using that particular phrase to explain to the reader how close he and Johnny are. The two boys have spent so much time together in close proximity that they think alike. Because they think alike, Johnny and Ponyboy do not have to say words to each other. They simply know what the other guy is thinking. It's not just thoughts that they understand about each other either. Both boys are capable of anticipating the needs and actions of the other person without anything needing to be said. What's great about their relationship is that Ponyboy and Johnny are not the only two Greasers that recognize this relationship. A few lines before your quote, Two-Bit teases Johnny and Ponyboy about their "telepathic" communication abilities.
Two-Bit always said he wondered why Johnny and I were such good buddies. "You must make such interestin' conversation," he'd say, cocking one eyebrow, "you keepin' your mouth shut and Johnny not sayin' anything."
Hinton/Ponyboy gives readers further evidence of Johnny's and Ponyboy's locked thought process in chapter six. When Dally stops the car in order to see the church burning, Ponyboy immediately hops out. He doesn't say a word to Johnny, but Johnny is out of the car at the same instant Ponyboy is.
I knew Dally would have to park the car and catch me before he could carry out his threat, and Johnny was already out and following me, so I figured I was safe.
When Ponyboy realizes that there are kids trapped in the church, he runs straight toward the church to help rescue the kids. He didn't look at Johnny. He didn't ask Johnny to come with. He just started running. Once at the church, Ponyboy was surprised by the fact that Johnny was next to him. The two boys didn't speak to each other at all, but both boys understood that they had started the fire and needed to help get the kids out.
I looked around, startled. I hadn't realized Johnny had been right behind me all the way.
In the Outsiders by S.E. Hinton Ponyboy said this, because they have a close relationship. Anyone who has a best friend knows that at times they can finish their friend's sentences. They can almost get into their heads. When someone says something funny you laugh, because you know your friend is thinking the same thing. They understand each other on many levels. It's as if they are becoming a mirror image of you, which they may start to do. The saying goes "you become who you hang out with". Ponyboy and Johnny like each other so much that they start becoming like the other.