Firstly, "Agile Development" is a loose term. There is an "Agile Framework" that is a collection of principles and ideas on how should software projects be managed. For details on the framework, you can visit http://www.agilemanifesto.org
Very broadly, Agile framework contrasts itself from earlier, traditional software development practices and methodologies. Main principles are:
- People across functional areas (programmers, testers, technical writers, sales, services, product managers) all work together as one team rather than different groups working in 'stages'.
- Iterative development (work in short development cycles with focused objectives)
- Incremental development (frequent releases to client)
- Focus on human communication
- High visibility of team's progress to management, stakeholders, clients
- Continuous feedback from customers and stakeholders
Based on these main principles, different methodoligies have been implemented. For example, Scrum, Extreme Programming, RUP etc. Note that Agile framework is a set of principles and guidelines, Scrum and Extreme Programming are concrete implementations of these principles that can be applied.
Agile methods are methods to manage teams and projects - these dont have anything to do with what software is developed or its architecture or design.
There are lots of details about Scrum and Extreme Programming available. Everything those processes define, you should be able to see one of the agile principles in effect.
So when it is said "Agile Development", it presumably means you have experience in working on a team or company that uses one of the methods implementing Agile framework.