SharePoint 2013 introduces a new way to extend sites using apps that can be self-contained, cloud-hosted, or provider-hosted. There are three types of apps: full page apps that fill the entire page, app parts that surface in an iframe, and extension apps that extend the ribbon or menus. Apps can be SharePoint-hosted using only HTML/JavaScript, auto-hosted on Azure, or provider-hosted using custom infrastructure. Apps provide benefits like increased stability, easier maintenance, and quicker delivery, but have limitations around server-side code and customizing SharePoint features.