$(function () {
  $("button:first").click(function(){
    $.ajax({
      url: "testAjax.php",
      type: "POST",
      data: моя_переменная_для_передачи_в_testAjax.php,
      timeout: 3000,
      beforeSend: function(){
        $("div").text("Загрузка...");
      },
      success: function(data){
        $("div").html("#table1");
      },
      error: function(xhr, status){
        $("div").html("<span>" + status + "</span>");
      }
    });
  });
});

.....
success: function(data){
        $("div").html("#table1");
......

....
<script type="text/javascript">

$(document).ready(function(){
     
$("#btn1").click(function(){
 var kriteriy=  parseInt(document.getElementById("in1").value);  
$.ajax({
  type: "POST",
  url: "source.php",
  data: 
  {
  
    param1:kriteriy
     
  },
  success: function(data){
    $("#div1").load("source.php #table1");
  }
});
});
});
</script>  
....

<table id="table1">
<tr>
<td>Code</td>
<td>Container</td>
<td>ETD</td>
<td>ETA</td>
<td>Criteria</td>
</tr>

<?php
$sql="select * from tblmonitoring where criteria=".$_POST["param1"];
mysql_connect("localhost","user123","pasword");
mysql_select_db("testdb");

$query=mysql_query($sql);
while($result=mysql_fetch_array($query))
{
echo "<tr><td>".$result['monitoringid']."</td><td>".$result['container']."</td><td>".$result['etd']."</td><td>".$result['eta']."</td><td>".$result['criteria']."</td></tr>";
}
?>

</table>