Hook to catch a variable in a POST request to a specific url?
You should use the services module to create an endpoint and use the url where is sent as the path to endpoint.

You don't state which type format the data is being posted to your site but the services module can handle many different types.

Also it's not stated exactly what you want to do with the received data but the services module can be set up to process it in a variety of ways.

You can capture it to a databse table etc 
or Here's an example of creating a node using services:
http://www.drupalwoo.com/content/blog/drupal-services-creating-node-from-external-form