To answer this question specifically, two problems:

  1. $randstring is not in scope when you echo it.
  2. The characters are not getting concatenated together in the loop.

Here’s a code snippet with the corrections:

function generateRandomString($length = 10) {
    $characters="0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ";
    $charactersLength = strlen($characters);
    $randomString = '';
    for ($i = 0; $i < $length; $i++) {
        $randomString .= $characters[rand(0, $charactersLength - 1)];
    }
    return $randomString;
}

Output the random string with the call below:

// Echo the random string.
// Optionally, you can give it a desired string length.
echo generateRandomString();

Please note that this generates predictable random strings. If you want to create secure tokens, see this answer.