"Agile software development is a conceptual framework for software engineering that promotes development iterations throughout the life-cycle of the project" Wikipedia says. But there is a much self-contained definition at agilemodeling.com: "Agile is an iterative and incremental (evolutionary) approach to software development which is performed in a highly collaborative manner by self-organizing teams with "just enough" ceremony that produces high quality software in a cost effective and timely manner which meets the changing needs of its stakeholders".
Agile development is all about making project done and working as fast as possible. It means that focus must be taken from some things and put to another. In this case "losers" are: prediction, documentation, processes, tools, contracts and plan. And the "winners" are: people, interactions, working software, collaboration, quick respond to changes. Let's see where it takes us.
Agile development appeared in 1990 as a result of heavy-weight project management approaches, that used in technology and required much resources and time. One of that approaches is Waterfall model, which passively flows the project over predefined stages. What is bad - it could be slow and not flexible at all. Some other models include but not limited to Cleanroom, Iterative, RAD, ScrumRUP, Spiral, XP, Scrum.
There is a document called "Manifesto for Agile Software Development" that is located at special website and allows to sign it whoever wants to. It is short and quick (as supposed to be for Agile) and says:
We are uncovering better ways of developing software by doing it and helping others do it. Through this work we have come to value:
Individuals and interactions over processes and tools
Working software over comprehensive documentation
Customer collaboration over contract negotiation
Responding to change over following a planThat is, while there is value in the items on the right, we value the items on the left more.
It describes the approach pretty clear, thou there are many sites in Internet, outlining it more specific. There are also a Principles of this approach, which disclose the needed focus position to get inside the model. The main idea is: Get things working, respond to changes and don't care too much about the rest.
But there is still a plan and management and goals and limits and so on. What makes Agile different is that only main goals are kept in mind always, throwing away not so important details and focusing on working software and satisfied customers. What is important and what is not - is described in Manifesto.
While Waterfall model is completely build on consciousness and prediction, the Agile model is alive and running. When Waterfall does it slow and stubborn, Agile dances. While Waterfall plans, Agile does. If we look at the World - we see that that the winner is one who "does". Perfectness is "a plus", not is "a must". What today is a must - is working stuff just on time.
This model is quite exciting and can make your and developer's life instantly get more "alive" and interesting, while the customers are satisfied and happy and the software is working great. Since it is done fast - the cash flow is all green too. If things go this way - no one will look behind and say "hey, that's not exactly what we planned at start", it just does not matter now.
So if you want to be more adaptive, flexible, fast and productive - you might want to get deeper inside the subject and find out more about techniques, that stand behind it.
There is Agile Alliance, organization, that took care about the model.
There is a on-line book from Martin Fowler "The New Methodology".
You can download PDF book "Essential Skills for Agile Development" (427 pages) at agileskills.org.
And there are other comprehensive sites about the topic you might want to read:
1. Using an Agile Software Process with Offshore Development
2. VersionOne
3. XPProgramming.com
4. Agile Development In 30 Seconds
5. Ten tips on agile software development
6. Good Agile, Bad Agile
7. The New Methodology
This article is written in Agile style itself - it gives you understanding about the topic, it is friendly and opened for collaboration, gives you the links for further research and took me not more than 30 minutes together with research and finding images :) And I got real pleasure on focusing on what is matter - delivering the needed knowledge to you and making it fast. Now you know it on practice is this what you want or not.

I've recently done some mini-research on Semantic Web and here what I found.