Based on your last comment, "i want it to be dynamic so as soon as the user clicks on something the relevant information will pop up", it sounds like you will probably want to use Ajax/JavaScript (I will demonstrate a simple jQuery example, notating for clarity):
<?php
$mydb = new mysqli('localhost','root','','TestTimeTableSolution');
?>
<html>
<!-- Add the jQuery library -->
<script type="text/javascript" src="//ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<script>
// Act when the document is ready
$(function(){
// listen for the select to change
$('select[name=TeacherID]').on('change',function(){
// Run the ajax – you can also use the shortcut $.post method found at:
// https://api.jquery.com/jquery.post/
$.ajax({
// This is the page that is going to do the data lookup/display action
url: '/lookup.php',
// This is how it's sending the data to that page
type: 'post',
// This is what is being sent ($_POST['submit'] in this case)
data: {
// Use $(this) to isolate the current selected element and get value (.val())
// The value is represented as $topic in your php
'submit': $(this).val()
},
// If all goes well and the page (lookup.php) returns a response
success: function(response) {
// Place the response into the div (see html snippet)
$('#loadspot').text(response);
}
});
});
});
</script>
<body>
<?php
$rows = $mydb->query("SELECT DISTINCT TeacherID FROM Teacher;")->fetch_all(MYSQLI_ASSOC);
$teachers = array();
foreach ($rows as $row) {
array_push($teachers, $row["TeacherID"]);
}
$dropdownMenu = "<select name='TeacherID' form='Teacher'><option value='Null' selected>All</option>";
foreach ($teachers as $topic) {
$dropdownMenu .= "<option value='" . $topic . "'>" . $topic . "</option>";
}
$dropdownMenu .= "</select>";
echo $dropdownMenu;
?>
<!---------------------------------------------->
<!-- THIS IS WHERE THE CONTENT WILL LOAD INTO -->
<!---------------------------------------------->
<div id="loadspot"></div>
</body>
</html>
In order for this to work, you need the page lookup.php in the domain root (you can make it whatever/where ever you want, but you need to match in the javascript url):
/lookup.php
<?php
# This is what will get placed into the parent page <div id="loadspot"></div>
# Do you your php here in place of this line and return whatever "relative information" you want
print_r($_POST);
You should review the jQuery page I have linked to to get more information and direction for that library and make sure you use your browser's developer tools to monitor javascript errors in the console. Ideally, you want to understand all this via the documentation instead of just copy and paste and move on...