Basic AJAX function in WordPress

ajax.js

jQuery(document).ready(function($){
	var ajaxurl = object.ajaxurl;
  	var data = {
    		action: 'my_action', // wp_ajax_my_action / wp_ajax_nopriv_my_action in ajax.php. Can be named anything.
		foobar: 'some value', // translates into $_POST['foobar'] in PHP				
	};
	$.post(ajaxurl, data, function(response) {
		alert("Server returned this:" + response);
	});
});

ajax.php

<?php
// embed the javascript file that handles the AJAX vodoo
wp_register_script( 'hip-ajax', plugin_dir_url( __FILE__ ) . '/ajax.js', array( 'jquery' ) ); 
// declare the URL to the file that handles the AJAX request (wp-admin/admin-ajax.php)
wp_localize_script( 'hip-ajax', 'object', array( 'ajaxurl' => admin_url( 'admin-ajax.php' ) ) );
wp_enqueue_script( 'hip-ajax'); 

add_action( 'wp_ajax_my_action', 'my_action_callback' );
add_action( 'wp_ajax_nopriv_my_action', 'my_action_callback' ); // for use outside admin

function my_action_callback(){
	$foobar = $_POST['foobar'];
	// do stuff here, for example wp_update_meta  
	echo "something"; // will be 'response' in ajax.js	
	die(); // this is required to return a proper result
}

No, hip-ajax is just the handle for the script and you can rename it into anything really.