Yes. This is a rather common question and you'd do good to take a look at the following questions as well:
How can I use JQuery to post JSON data?
Jquery Ajax Posting json to webservice
Essentially, you use a client-side language (Javascript) to send a POST request to your backend. Naturally, you will then require a backend language (such as PHP or node.js).
I'll provide an example:
JS (jQuery):
$.post("http://yourURL.com/backend.php",{
data: {
"name" :"John Smith",
"vehicle":"TARDIS"
}
}).success(function(response){
console.log(response)
//do something with the response
});
PHP
<?php
$data = json_decode($_POST['data'], true);
$name = $data['name'];
$vehicle = $data['vehicle'];
echo "Welcome {$vehicle}-driving $name!";
?>
Your PHP especially should include error checking among other things, but this will suffice for a simple example.
In your console, upon executing the AJAX request you will then see the following:
Welcome TARDIS-driving Doctor!
Which is the output from your PHP file