Design Manager is a part of SharePoint Server 2013 Standard and Enterprise offerings. You can use
SharePoint Design Manager
to overhaul the design of the SharePoint site by using custom HTML pages. This helps you in branding and styling your site based on your requirements. You could also make use of any HTML editor.
SharePoint Design Manager comes free with Standard and Enterprise editions
The Standard and Enterprise editions of SharePoint allow the users to access all the features of the Design Manager, which is a distinct improvement over SharePoint Designer. Design Manager needs Publishing feature which is a part of SharePoint Server 2013 Standard and SharePoint Server 2013 Enterprise.
Besides, the Standard or Enterprise editions of SharePoint also allow you to install apps from the Internal Catalog or the public SharePoint Store. Similarly, cloud-hosted and SharePoint-hosted apps can be installed on the Standard or Enterprise editions. These are not possible with the Foundation edition of SharePoint.
Apart from SharePoint Design Manager features, the Standard or Enterprise editions feature Project Site Templates, Asset Library Enhancements/Video Support. An Asset Library is pre-configured to use special features that help users manage rich media assets such as image, audio, and video files.
You can read more about the other features of SharePoint Standard here, and SharePoint Enterprise here.