Agile Development

Agile is software development methodology. It is very effective where Client frequently changes his equirement. Since it has more iteration so you can assure a solution that meets clients requirement.
More than one build deployment for a project. It involves more client interaction and testing effort.
There are two methods by which this methodology can be implemented:-
1- Scrum.
2- Extreme Programming.

Scrum: Each iteration would called a scrum which can be a 1- 2 Months. In Scrum Client prioritize his requirements what he want first. If developer did not meets all the requirement which was being fixed for a particular scrum than rest of the development part would be transferred to the next scrum (would be delivered in the next build), means developer can't increase time decided for a scrum. Its fixed.
Extreme Programming (XP): here iteration period would be less then in scrum , which is being 2-4 weeks.
Here developer prioritize what to do first on the basis of client requirement. This duration which was being fixed for a iteration, can be increase if the some development part is still pending. The build would deployed with having all the client needs. Thus iteration period is not fixed here it can be increase but iteration should meets all the client's requirement in this build.
More attention is required for testing in XP.

Apart from all the above answers, just add this important point.
There are many flavors of Agile Development:
1- Agile Manifesto
2- (XP) Extreme Programming
3- Scrum
4- Crystal
5- Context Driven Testing
6- Lean Development
7- (Rational) Unified Process

Agile methodology is a conceptual framework where software is developed in iterations. Each iterations has Requirement analysis, planning, design, coding, testing and documentation.
Characteristics:
- Many builds are delivered in the iteration process
- Accepts change of requirement at any stage
- Requires close communication between business,
Development and Testing people
- Reduced risk and time to develop
- Less documentation work compared to other methodologies
- Requires continuous testing

Test Driven Development
http://www.javacodegeeks.com/2012/05/test-driven-development-win-win.html