When you have added a destination URL to your account where you want to receive the Kartra API's outbound pings, you will need a script to catch and interpret the data. Make sure it's written in a programming language that can catch the HTTP raw post request.
Here is a small PHP sample on how to get the raw post:
$postdata = file_get_contents("php://input");
// the data comes as an json so you will need to decode it
$postdata_decoded = json_decode($postdata);
// after this you can use the info passed from kartra in your own scripts.
// Ex: $postdata_decoded-lead contains the lead details that triggered the action
?>