It means that as you move functionality (not data) between the server and the client, you need to rewrite your code. For example if you do input validation, you need to write the same code twice: once in {Java, Python, Ruby} or whatever the server side language is, and the second time in JavaScript so you can alert the user that the data in some fields doesn't pass the checks.
This is not a problem if you are using GWT, or if you do serverside programming in JavaScript.