Agile Development proposes an adaptive model for development as a counterproposal to (or improvement on - perspective) the less flexible, traditional approaches like the Waterfall Model.
Simplified, the main difference between the approaches is that Agile loops through many iterations of the process, connected through Feedback Loops that start the next iteration, whereas traditional methods run through a single iteration and omit the feedback loops.
In practical terms, this means: At the end of an iteration (e.g. a Scrum Sprint), the customer / user can be involved and their feedback can be incorporated in the next iteration.
As any organizational pattern: Agile is an attempt to orchestrate medium to enormously large groups of people to move efficiently in roughly the same direction.