Try this:
$(".wrapper .button").click(function (event) {
event.preventDefault();
$(this).parent().append('<span> This content will be added </span>');
});
FIDDLE DEMO
Using your code:
$('.wrapper').append('<span> This content will be added </span>');
Append the new content to all the div with .wrapper class. We need to firstly get the button in the current scope of the click event using this. After, that we will get its parent using $(this).parent() and then append the new content only to that specific div.
UPDATE
A much better code would be using the closest() here:
$(".wrapper .button").click(function (event) {
event.preventDefault();
$(this).closest('.wrapper').append('<span>This content will be added</span>');
});
Now, closest('.wrapper') will get the first element that matches the .wrapper selector by testing the element itself and traversing up through its ancestors in the DOM tree and making sure non-immediate descendants are not selected.