All it does is find a string within another string.
Let's take an example:
Assume you have a website named http://www.MyWebSite.com
And a script named TestIt.php as shown below:
<?php
echo $SERVER['PHP_SELF'] . "<br />";
$url = "TestIt.php";
$retVal = strpos($SERVER['PHP_SELF'], $url);
if ($retVal == FALSE)
echo $url . " not found in " . $_SERVER['PHP_SELF'] . "<br />";
else
echo $url . " found in position " . $retVal . "<br />";
?>
So if you ran the code above, you would get the following output:
/MyWebSite.com/TestIt.php
TestIt.php found in position 15
Now if you changed $url to "MyWebSite.com", strpos would return 1
Make sense?