Exporting your boundaries or projects is a very useful feature if you wish to work in other GIS type programs. It is also a way to move projects from one map to another.
You are only exporting the boundary or project details you have created, the export does not include the base map.
In the top right of the screen click on Export.
The export menu will open. Select what you would like to export then pick your Export as option from GeoJSON, KML or Shape file select, click export.