I found 1 syntax error in your code.
You have error here
<?php echo $result[$objResult["url"];?>
which should be 
<?php echo $result["url"];?>
check my code.
<?php
    ini_set('display_errors', 1);
    error_reporting(~0);
    $serverName = "localhost";
    $userName = "root";
    $userPassword = "";
    $dbName = "mydatabase";
    $conn = mysqli_connect($serverName,$userName,$userPassword,$dbName);
    $sql = "SELECT * FROM customer";
    $query = mysqli_query($conn,$sql);
?>
<table width="600" border="1">
  <tr>
    <th width="91"> <div align="center">URL </div></th>
    <th width="98"> <div align="center">Board </div></th>
      </tr>
<?php
while($result=mysqli_fetch_array($query,MYSQLI_ASSOC))
{
?>
  <tr>
    <td>
        <div align="center">
        <?php echo $result["url"];?>
        </div>
    </td>
    <td><?php echo $result["board"];?></td>
  </tr>
<?php
$sql2 = "INSERT INTO data (url,board) VALUES ('".$result["url"]."','".$result["board"]."')";
$query2 = mysqli_query($conn,$sql2);
}
?>
</table>
<?php
mysqli_close($conn);
?>
dont forget to change your connection parameters. 
here is the SQL Script : 
DROP TABLE IF EXISTS customer;
CREATE TABLE customer (
  id int(11) NOT NULL AUTO_INCREMENT,
  url varchar(255) DEFAULT NULL,
  board varchar(255) DEFAULT NULL,
  PRIMARY KEY (id)
) ENGINE=InnoDB AUTO_INCREMENT=4 DEFAULT CHARSET=latin1;
-- Records of customer
INSERT INTO customer VALUES ('1', 'First URL', 'Bord 1');
INSERT INTO customer VALUES ('2', 'Second URL', 'Board 2');
INSERT INTO customer VALUES ('3', null, null);
-- Table structure for data
DROP TABLE IF EXISTS data;
CREATE TABLE data (
  id int(11) NOT NULL AUTO_INCREMENT,
  url varchar(255) DEFAULT NULL,
  board varchar(255) DEFAULT NULL,
  PRIMARY KEY (id)
) ENGINE=InnoDB AUTO_INCREMENT=11 DEFAULT CHARSET=latin1;
-- Records of data
INSERT INTO data VALUES ('1', 'First URL', 'Bord 1');
INSERT INTO data VALUES ('2', 'First URL', 'Bord 1');
INSERT INTO data VALUES ('3', 'Second URL', 'Board 2');
INSERT INTO data VALUES ('4', 'First URL', 'Bord 1');
INSERT INTO data VALUES ('5', 'Second URL', 'Board 2');
INSERT INTO data VALUES ('6', 'First URL', 'Bord 1');
INSERT INTO data VALUES ('7', 'Second URL', 'Board 2');
INSERT INTO data VALUES ('8', 'First URL', 'Bord 1');
INSERT INTO data VALUES ('9', 'Second URL', 'Board 2');
INSERT INTO data VALUES ('10', '', '');