$("#add_button").click(function(){
var intial_field = $(this).data("intial");
var content = '<div id="input_'+intial_field+'"><input type="text" name="user_name[]" /><button id="remove_btn" data-remove="'+intial_field+'">X</button></div>';
$("#recurssion_container").append(content);
$(this).data("intial",intial_field+1);
});
$(document).on("click","#remove_btn",function(){
var remove_element = $(this).data("remove");
$("#input_"+remove_element).remove();
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<button type="button" id="add_button" data-intial="0">+ Add</button>
<form action="index.php" method="post">
<div id="recurssion_container"></div>
<input type="text" name="user_name[]" />
<button type="submit" name="save">Save</button>
</form>
<?php
if(isset($_POST["save"])){
$user_name_array = $_POST["user_name"];
foreach($user_name_array as $user_name){
if($user_name!=""){
#Put your insert query here
#Please refer how to save data to database https://www.w3schools.com/php/php_mysql_insert.asp
}
}
}
?>