You are misunderstanding event delegation. Event delegation is done with the closest div. Here I have used document but you can use the closest div to use it as event delegation.
Use this:
$(document).on('change','.check-input',function(){
$(this).next().text('Error');
});
demo
here's the link to understand about the event delegation
Example:
// attach a directly bound event
$( "#list a" ).on( "click", function( event ) {
event.preventDefault();
console.log( $( this ).text() );
});
// attach a delegated event
$( "#list" ).on( "click", "a", function( event ) {
event.preventDefault();
console.log( $( this ).text() );
});