A callback URL is an address that a server provides, and any computer in the Internet/private network can POST data to it.
This method is more efficient than a computer continuously waiting or polling for data. For example when the Post Office gives you an address box where the whole world can send you letters, you do not have to be there to receive. You can just periodically check for your mail. For this to work, you have to share your address with anyone interested in sending you mail. In addition, everything you receive has to also be appropriately packaged in the rules that the PO gives (i.e size, weight, stamp etc). This is similar to how a call back works. You have to set up the call back in the way that the sender of the data you want specifies. E.g. a call back for Facebook to receive data from FB is different to how you will set up a call back to receive data from AT.
At Africa's Talking we use callback URLS for: -
To send notifications on the status of messages sent out
To send notifications on the status of airtime sent out.
To notify you whenever a user sends a message to your Premium Short Code. In response you can send as a message to forward to them.
To notify you whenever a user dials your USSD code. In response, you can send us a menu that the user will see and reply to.
To notify you whenever a user calls your phone number. In response, you can send us instructions (in XML format) on how to handle the call and we will do the rest.
You may have a look at our article on how to configure a callback URL for various products.