You can save a file in XML format using Save As on the File menu and selecting XML puzzle under Save as type. If you want to exclude solution or citation/explanation information from the exported file, you can also the additional XML export options under Export on the File menu.
XML is a standardized extensible format for exchanging data; other programs may be able to read and manipulate XML files. You can open an XML puzzle file with Crossword Compiler as you would a normal file. Note however that the XML format does not include all the possible constructor settings of the default file format; it does however cover essentially all properties required by solving programs
The interactive puzzle applet supplied with Crossword Compiler uses an XML file format (encoded in javascript). Puzzles created for use with the solving applet can also be opened with Crossword Compiler.
Puzzles saved as XML using Save As do not include additional layout options required by the solving applet. However, the file does include full solution information, which will not be the case if you export a web crossword without solution information.
The basic XML format is documented in an .xsd file at https://crossword.info/xml/rectangular-puzzle.xsd. Applet files generated by Crossword Compiler contain additional information relating to applet formatting etc.