Here's the example given on Wikipedia:
John asked Mary to wash him.
In this sentence, we could interpret that John and him are the same person, so there's no 'binding' violation here. (Equally, it may be that John and him are different people.) Now look what happens if we swap the two words:
He asked Mary to wash John.
With this word order, we cannot interpret that He and John are the same person. There's a violation of the rule that allows us to identify one thing with another.