XSLT stands for Extensible Stylesheet Language Transformations and enables transforming XML documents into other formats like HTML. XSLT uses XML documents called stylesheets that contain elements and attributes to define templates that match elements in the XML data and specify how to transform their contents. Transformations can occur on a server, client, or with a standalone program and involve elements like <template> to select nodes, <apply-templates> to process children, <value-of> to retrieve node values, <for-each> to loop through nodes, and <sort> to sort output.