The menu form field type provides a drop down list of the available menus from Joomla site. If the field has a saved value this is selected when the page is first loaded. If not, the default value (if any) is selected. The first option on the list is always '- Select Menu -' (which is a translatable string) and is given the value 0.
Example XML field definition:
<field name="mymenu" type="menu" default="mainmenu" label="Select a menu" description="" />