As mentioned above, Shopify 2.0 is the better integrated successor to the original Shopify Online Store. A lot of work has been done to improve performance metrics and to make it much easier to use in partnership with the Shopify App Store to build out the functionality you need while retaining the levels performance your customers expect.
Shopify 2.0 upgrading is simply the migration of your site from one code-base to another and making sure your theme and page templates migrate seamlessly to the new architecture, allowing you to take full advantage of the improvements that have been made (not just since Open Store was released, but also in the interim period since the launch of 2.0).