What is SharePoint Application catalog? and where do we use this?
The App Catalog is a site with the purpose of making apps (internally developed or third-party) available for users to install.
Maybe one of the coolest features is that you can install apps from the App Catalog to your sites, without going to each individual site.
You use the App Catalog by creating a new App Catalog site, and then add the Apps you want users to be able to download to the site.
Actually, Microsoft has excellent documentation regarding this: http://office.microsoft.com/en-us/sharepoint-help/use-the-app-catalog-to-make-custom-business-apps-available-for-your-sharepoint-online-environment-HA102772362.aspx
The link even contains information about how to set it up, and add apps you, or a third-party developer has developed.