What is Agile methodology and what is the expected result of Agile?

Agile methodologies are a collection of methodologies aimed at accelerating business results and increasing transparency around progress to organizational stakeholders.  While commonly applied to software development, agile techniques have been applied with great success to business consulting, governance, R&D, and a multitude of other organizational initiatives where rapid business results and high degrees of collaboration are desirable.
Typical results expected on agile projects include:
1. Acceleration of delivery,
2. Better alignment of project results with actual business needs,
3. Increased involvement in the solution by business owners,
4. Higher quality driven through earlier and more frequent tests,
5. Increased employee morale through a focus on predictable, efficient results without excessive overtime.