Assuming you're using Apache, this can be done using something called URL rewriting. Create a file called .htaccess in your document root, and add this:
# Turn URL rewriting on
RewriteEngine on
Options +FollowSymlinks
# Rewrite rule
RewriteRule ^(\d+x\d+)/?$ index.php?dimensions=$1 [L]
The first two lines turn the rewrite engine on, and the third line defines a RewriteRule. The first part ^(\d+x\d+)/?$ is a regular expression that the part of the URL after the domain will be matched against.
The second part index.php?dimensions=$1 is the URI that will be rewritten to. The client doesn't see this, but PHP will.
If I do a print_r($_GET) in index.php with the URL http://localhost/400x300, I get this:
Array ( [dimensions] => 400x300 )
This is from the standard $_GET superglobal array in PHP and can be used as normal. URL rewriting leaves the URL as it is in the browser, yet allows you to turn it into one usable by PHP with a query string.
To make your script a bit easier to use, you could split the expression up to get separate X and Y values:
RewriteRule ^(\d+)x(\d+)/?$ index.php?x=$1&y=$2 [L]
Which will give an array like this:
Array ( [x] => 400, [y] => 300 )