Below is the excerpt from Wikipedia for the definition of Agile Software Development:
Some of the principles behind the Agile Manifesto are:
- Customer satisfaction by rapid, continuous delivery of useful software
 - Working software is delivered frequently (weeks rather than months)
 - Working software is the principal measure of progress.
 - Even late changes in requirements are welcomed.
 - Close, daily, cooperation between business people and developers
 - Face-to-face conversation is the best form of communication.
 - Projects are built around motivated individuals, who should be trusted
 - Continuous attention to technical excellence and good design.
 - Simplicity
 - Self-organizing teams
 - Regular adaptation to changing circumstances
 
- The culture of the organization must be supportive of negotiation
 - People must be trusted
 - Fewer but more competent people
 - Organizations must live with the decisions developers make
 - Organizations need to have an environment that facilitates rapid communication between team members
 
- lack of structure and necessary documentation
 - only works with senior-level developers
 - incorporates insufficient software design
 - requires too much cultural change to adopt
 - can lead to more difficult contractual negotiations
 
- Extreme Programming (XP)
 - Industrial Extreme Programming(IXP)
 - Scrum
 - Agile Modeling
 - Adaptive Software Development (ASD)
 - Crystal Clear and Other Crystal Methodologies
 - Dynamic Systems Development Method (DSDM)
 - Feature Driven Development (FDD)
 - Lean software development
 - Agile Unified Process (AUP)
 - Dialogue-Driven Development aka d3