Agile development is a flashy term for developing a system in a common-sense way: start with the highest priority features, avoid taking on too many different features at the same time, keep each development phase short and re-evaluate frequently.
Agile development is popular today because it works and delivers results quickly.
Your requirements are ordered by priority and bundled together into separate phases (called sprints). A sprint is usually completed in 3-4 weeks (but depends on project size). Once completed it will be tested and uploaded. You and the development team will then evaluate what features to include in the next sprint. The benefits are:
Most work at LiteBreeze is carried out in iterations of 150-200 man hour sprints. Together with the client we are forced to select the most important features. We've found that this pushes development forward quickly. Time is not wasted on medium-priority features that may change or be discarded anyway.
If you only need a few hours of work done every now and then, then this concept will not really be used.