Usually refers to package interdependencies in O/S
distributions such as
RedHat and
Debian. If package B predepends on package A, that means you have to install package A before you can install package B. It also usually means that if you install packages A and then B, that removing A will "break" B. For example, if MyGroovyProgram predepends on code libraries contained in ncurses and I remove ncurses, MyGroovyProgram won't be able to run until ncurses is re-installed. Package managers usually know this and won't let you break a predependency without at least warning you.
Other examples: Legally driving a car predepends on having a drivers' license, insurance, and current registration for your car. Taking communion in a Catholic church predepends on being officially confirmed into the religion.