A context diagram shows the relationship between a system and external entities, with the entities providing inputs to the system and receiving outputs from it. Context diagrams are important for software engineering as they provide an overall view of the system and how it interacts with different elements and entities. Developing a context diagram helps ensure all entities belong to the system, which allows for complete development and refactoring. Analyzing the context diagram allows engineers to predict how the system works, anticipate errors based on inputs and outputs, and determine if the system is functioning properly.