It works by allowing you to process a Webhook from Shopify and subscribe the purchaser to a specific MailChimp list. In a nutshell, Webhooks enable you to collect information about events as they happen in near real-time. (read more about the MailChimp API and Webhooks here)
You can grab the plugin and installation instructions here. Then, all you need to get started is your Shopify Shop ID and MailChimp List ID.
Use another ecommerce or shopping cart solution? MailChimp also currently intergrates with Magento, osCommerce, PrestaShop, Foxy Cart and ZenCart. Be sure to take a look at our extensive list of plugins for more info.