I'm not a teacher, but I'll try to explain the meaning I get.
When someone makes a promise, only to break it, someone else gets hurt.
Now, the first one aplogizes, but "an apology is nothing but words, the same way the promise was".
Maybe he was lying from the start and he's saying than this apology isn't sincere either.
Words are useless to heal a wound, even if you're honest. And when someone is hurt because you didn't keep your word, your words of apology are worth less than hot air.