Debian has two menu systems:
The official one is the FreeDesktop Desktop Menu Specification, which was adopted as the primary menu in Gnome, KDE, LXDE and others. It is famous for the *.desktop files in /usr/share/applications. The chapter 9.6 of the Debian Policy covers its use.
The original Debian menu system, now optional, provides a centralized list of all installed user applications (for which the packager provided a menu entry). It is a documented in the DebianPolicy. Those menu entries are available in most window manager / Desktop environment in Debian (KDE, GNOME, ?GNUStep, ?Enlightenment and ?Windowmaker, making every application available in every environment). Each application drop a menu entry in /usr/share/menu/ and menu manager register to menu by dropping an entry in /etc/menu-methods/.
In 2014 the Debian technical committee was asked to choose between these two menu systems (741573) and in September 2015 it decided that the preferred menu system is the FreeDesktop one.