Files with the extension DOTM contain a macro-enabled Open XML Document Template, ie a template for Microsoft Word documents. These files contain various formatting information, such as margins, headers, footers, and fonts and margins. They can be used to create several documents with the extension docm, all of which share the same style. This is useful for business letters, etc., for example. Unlike dotx files, these templates can also contain macros.
Microsoft supplies with Word some templates, but many templates are also available for free or to buy Kuflich.
The DOTM files are used by Microsoft Word as of version 2007 (Mac 2008). The older versions use the dot extension for their template files.