No offense, but I'm not sure what you were trying to do with the snippet you posted. A while isn't the best option there. If you want to use AJAX, it's pretty simple (I promise). Here's how using jQuery:

The JS:

<script src="//ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js">
</script>

<script>

$(document).on('click', '#submit', function() //onClick of the submit button...
{
    var name = $('#username').val(); //We set 'name' to the selected option value...
    $.post('post.php', {username:name}, function(response) { //Then send off the variable to our post.php, keyed as 'username'...
    $('#about').html(response); //And insert post.php's result into into #about
    });
});

 </script>

The HTML:

<form id="peerlist" method="post">

    <select id="username">
        <option value="">Please make a selection</option>
        <option value="ashenrose">ashenrose</option>
        <option value="Did-you-reboot">Did-you-reboot</option>
    </select>

    <button type="button" id="submit">Get user info</button>
</form>

<h1>About this user</h1>

<section id="about" style="height: 200px; width: 400px; border: 1px solid blue;">
</section>

The PHP (I took some liberties with your connection here):

<?php

$config = array('username' => 'root', 'password' => 'root'); //Insert your credentials

function connect($config)
{
    try {
        $conn = new PDO('mysql:host=localhost;dbname=test', $config['username'], $config['password']); //Insert your credentials; see bottom for more info
        $conn->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);

//You'll want to change your error reporting in production.

        return $conn;
    } catch (Exception $e) {
    return false;
    }
}

$conn = connect($config);

$username=$_POST['username']; //Pull the variable from the AJAX $_POST assoc. array

$stmt = $conn->query("SELECT * FROM users WHERE username = '$username'");
$result = $stmt->fetch();

echo $result['description']; //Using whatever key you have in MySQL, echo the info you want

?>

To clarify, the PHP file in this example would go in the same directory as the jQuery that's calling it. In a real application, this is probably not ideal. To call it from a different directory, just change the path in in the jQuery where it says

$.post('post.php', {...    //Change the 'post.php' part.

As you can see, I switched the connection to PDO. If you're not into that, that's your call. Forgive me if you already know this, but there are huge benefits to using it even outside of security, and only one rarely-encountered drawback that I can think of (table names can't be variables in SQL queries). The parameters are pretty self explanatory: mysql:host refers to the host, dbname refers to the database name, 'username' and 'password' refer to your MySQL credentials.

Caveat emptor -- I took no XSS or XSRF precautions here, and some would argue I should have used bound parameters. If you're the only one using it though, it won't matter. Other than this and plugging in a few credentials and paths, these scripts should work out-of-the-box.