When the callback is fired, an instance of the template has been rendered (added to the document). It can be useful if you for example want to manipulate the elements in the template through the use of a JavaScript library, for example CodeMirror, as I used in one of my projects. For example:
<template name="test">
<textarea></textarea>
</template>
Template.test.rendered = function(){
// Make the textarea highlight the code (kind of).
var myCodeMirror = CodeMirror.fromTextArea(this.find('textarea'))
}