dmenu is a suckless program and a lot of tiling window managers (eg. i3, dwm) use it as default application launcher.

dmenu_run is a shortcut for dmenu_path | dmenu "$@" | ${SHELL:-"/bin/sh"} &. When you invoke your dmenu command, dmenu_run will start by default. At its place (which dmenu_run) - usually usr/bin - one can easily hack dmenu or create an alternative for the default. Try out from a terminal:

dmenu_path | dmenu -b "$@" | ${SHELL:-"/bin/sh"}

Spoiler: -b option puts the menu to the bottom of the desktop. Just a small step for the mankind.