It means: "decided that it would not be a good idea (and so did not do it)". The phrase is idiomatic and so analysing the individual words will probably not help you to understand and use it well. You could try to think of a similar situation in your life and practice by writing a short para about it.

"It" in this sentence refers to whatever it was that "he" wanted to say. To "think better of something" means to decide not to do/say something, often because you realise it will have a bad outcome of some kind