Used to hook an ajax action to server function when a user is not logged into the front-end,

add_action('wp_ajax_nopriv_front-end-action', 'server_function');
function server_function(){
	//validate a nonce, and other $_POST data elements and execute some code.
	wp_json_send($data); //use wp_json_send to return some data to the client.
	wp_die(); //use wp_die() once you have completed your execution.
}

On the front-end you would have some js script executed based on some event,

//some event on the page would trigget the following 
var data = {
  'action' : 'front-end-action',
  //some more data to pass to the server...
};
//send the data to the server using the jQuery post method
//note for the ajaxurl, its best to set it dynamically using the wp_localize_script function, see the link below
 $.post(ajaxurl, data, function(response) {
  //handle the response from the server
});

for more info, checkout https://developer.wordpress.org/plugins/javascript/ajax/