INDD is the document extension for an Adobe InDesign Document file. These files can be opened an edited using the Adobe InDesign software which is available from https://www.adobe.com/indesign
Adobe InDesign is the leading software for laying out professional looking documents, and is commonly used in marketing and communications teams, as well as for producing bids and tenders, company reports and more.
Other file types which are associated with InDesign include INDT which is the format for an InDesign Template and IDML which is the InDesign mark up language.
How does INDD differ from IDML and INDT?
INDD files are InDesign documents and this is the standard file type for anybody saving a document within InDesign. These files can be opened on the version of InDesign they are created in or later, but are not generally backward compatible and as such can not be opened on earlier versions of InDesign. If you need your document to be saved on an earlier version of InDesign then you are better saving it as an IDML file.
IDML files are InDesign markup language files. These can be opened on any version of InDesign back to InDesign CS4 as they are a backward compatible XML based format. As such an IDML version of the document is often included when sending files between clients and their agencies, in order to ensure that it can be easily opened on older versions.
INDT files are InDesign template files. These are basically InDesign Documents however when you go to File / Save they force you to give the document a new name, where as an INDD file will simply write over the old file. This is ideal where you want a reusable template that won't easily be written over by accident.