Hi there!
Many of Jetpack’s features rely on WordPress.com servers to power them. That is why the connection to WordPress.com is required. For example, resizing images for Tiled Galleries is done on our servers. This actually reduces the load on your server, and will improve your site’s performance.
Jetpack also stores some data from your site on our servers:
– All your public posts (non password-protected, non private) are synchronized with WordPress.com servers. This allows Jetpack to send out subscription emails and publish links to these posts on your Social Network profiles (if you use Publicize).
– Your subscribers’ email addresses are also stored on WordPress.com servers, since the emails are sent from there. That’s why Automattic’s Privacy Policy applies to Jetpack too. You might want to mention this Privacy Policy in your terms of service.
– Your stats, and some of your site settings (like your site URL, your site’s permalink structure, language, etc.) are also stored on WordPress.com servers.
All this information is attached to your site URL on WordPress.com, so if you disconnect from a WordPress.com account and reconnect with another, your data will be back as long as you do not change your site URL.
Lastly, Jetpack is entirely free; we won’t charge you money for any of the modules included (other than for the VaultPress service, which you can sign up for through Jetpack).
I hope this helps to clear things up! Don’t hesitate to let me know if you have any additional questions.