you are adding the event click to input.apagar before creating the same.
then put the evento to all the input.apagar pertaining to #content using the method $.on.
Another detail, the $.parents will fetch all relatives, so if in your HTML tree you have more than one span above the input.apagar it will also be deleted, so use the method $.parent, After all you only want the first span.
$(document).ready(function(){
    var add = $('.add');
    var content= $('#content');
  
    add.click(function(){
        content.append('<div><span> <input type="text" name="nome" value="Cópia" /> <button class="apagar">Apagar </button></span></div>');
    });
    content.on("click", "button.apagar", function(event){
        $(event.target).parent().parent().remove();
    });
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<div id="content">
  <div>
    <button class="add">Adicionar outro campo</button>
  </div>
  <div>
    <span>
      <input type="text" name="nome" value="Original" /> 
      <button class="apagar">Apagar </button>
    </span>
  </div>
</div>
 
 
here is an adaptation of the @Gabrielrodrigues solution
$(document).ready(function() {
  var add = $(".add");
  var content = $('#content');
  var onApagarClick = function() {
    $(this).parents('span').remove();
  };
  add.click(function() {
    var novaLinha = $('<span> <input type="text" name="nome" value="Cópia"> <button class="apagar">Apagar </button></span> <br>');    
    $('.apagar', novaLinha).click(onApagarClick);
    $('#content').append(novaLinha);        
  });
  $('.apagar').click(onApagarClick);
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>
<div id="content">
  <div>
    <button class="add">Adicionar outro campo</button>
  </div>
  <div>
    <span>
      <input type="text" name="nome" value="Original" /> 
      <button class="apagar">Apagar </button>
    </span>
  </div>
</div>
 
 
							
							
						 
The problem is the scope, put the delete inside the add click that will work.
– Gabriel Rodrigues
Thanks, you helped me out
– Amanda Lima