You want to replace apple! with apples! but in your text area you have only apple and not apple! (with exclamation mark). So please add ! to your text area or remove from input fields and try below code
$(function(){
$('#replaceBtn').click(function(){
var findText = $('#find').val();
var replaceText = $('#replace').val();
var inputText = $('#input').val();
inputText = inputText.replace(findText, replaceText);
$('#input').val(inputText);
});
});
JSFiddle Demo
NOTE - Assuming that you are doing this replace on some button click. I have used Replace button in my demo. Also note that this replace is case sensitive.
EDIT - Above solution will replace only first occurance of word, to replace all occurrences you need use RegEx hence replace below line
inputText = inputText.replace(findText, replaceText);
with
inputText = inputText.replace(new RegExp(findText, 'g'), replaceText);
JSFiddle Demo with RegEx