Waterfall is a software project management method by which a project is developed in a series of stages of:
It is a widely-hated process of working, especially in games, because it treats the project as a set of certainties and development as essentially an act of translation. The reality of most game projects is that they are often trying to discover a game dynamic which works (called 'finding the fun'), which is an inherently sloppy and experimental process. As such most developers prefer to work in an agile (either formally or informally) fashion.
However most contracts between developers and publishers are formulated in a quasi-waterfall fashion, mandating milestones such as game design documents and deliverables such as assets or functionality on a timetable. The reason they do it this way is that waterfall tends to give the illusion of certainty and is the easiest method to explain at the executive level. The reality of working this way, however, is waste, cancelled projects and crunch.