An external form is used outside the panel, for a user, which has not been logged in the control panel. For example, this can be a "License activation" form. This form is much similar to a common form, but it doesn't have the "Cancel" button.
The extform.xsl template is used for the external form.
You can use TESTmanager for tests. Call any form, and add the stylesheet=extform parameter to the call. E.g. the "User settings" form TESTMGR_URL?func=usrparam&stylesheet=extform