Explain the agile process, methodology, model, etc.

"Agile" is a methodology, a model, a process, and a philosophy, depending on context. The Agile Philosophy is best summed up by the Agile Manifesto linked in Neil's answer. It's a statement of relative values that are used to guide agile methodologies. Agile Methodologies are methodologies that build on and formalise the agile philosophy into something concrete a development team can use to guide their practises. An Agile Development Model is a set of practises as part of an agile methodology that form a guideline for software development and testing. The terms "model" and "methodology" are often used interchangeably, but there is a subtle difference: a methodology is the theoretical statement of practises, where a model is the practical guideline to actually implementing those practises. An Agile Process is any process implementing an agile development model. There are numerous examples: Scrum, XP, Kanban... All of them will be called "agile" depending on context.