Scrum is a subset of Agile. It is a lightweight process framework for agile development, and the most widely-used one.
A “process framework” is a particular set of practices that must be followed in order for a process to be consistent with the framework. (For example, the Scrum process framework requires the use of development cycles called Sprints, the XP framework requires pair programming, and so forth.)
“Lightweight” means that the overhead of the process is kept as small as possible, to maximize the amount of productive time available for getting useful work done.
A Scrum process is distinguished from other agile processes by specific concepts and practices, divided into the three categories of Roles, Artifacts, and Time Boxes. These and other terms used in Scrum are defined below. Scrum is most often used to manage complex software and product development, using iterative and incremental practices. Scrum significantly increases productivity and reduces time to benefits relative to classic “waterfall” processes. Scrum processes enable organizations to adjust smoothly to rapidly-changing requirements, and produce a product that meets evolving business goals. An agile Scrum process benefits the organization by helping it to
Increase the quality of the deliverables
Cope better with change (and expect the changes)
Provide better estimates while spending less time creating them
Be more in control of the project schedule and state