According to MSDN:
An app for SharePoint is a web application that is registered with SharePoint using an app manifest. An app manifest is an XML file that declares the basic properties of the app along with where the app will run and what to do when the app is started.
Apps for SharePoint are self-contained pieces of functionality that extend the capabilities of a SharePoint website. Apps integrate the best of the web and SharePoint; they are targeted, lightweight, and easy-to-use, and do a great job at solving a user need. Users discover and download apps from the SharePoint Store or from their organization's private App Catalog and install them on their SharePoint sites.
Through apps in SharePoint 2013
SharePoint 2013 apps can be hosted in 3 different places like:
2- Host in the cloud:
SharePoint automatically deploys the app into Windows Azure Web Sites and SQL Azure, and these apps run in the cloud.
3- Can be hosted in mix components in SharePoint and cloud:
SharePoint components run in SharePoint, and components hosted in the cloud run in the cloud.