As I mentioned in my earlier post, Agile Modeling and Iterative Development, I have purchased Agile & Iterative Development - A Manager's Guide as well as Applying UML and Design Patterns. Both books are written by Craig Larman and pretty easy to read.
Agile and iterative development breaks software development into several mini-projects, each one being a self-contained, fully tested, and high quality subset of the final project. Many of these iterations might be internal deliveries, but the key is to have customer involvement after each iteration to receive critical feedback and direction.
The iterations typically run anywhere from 1 to 6 weeks. From a very high-level perspective, each iteration may start with requirements gathering for that iteration as well as modeling done on white boards, etc. Once completed, most of the time is then spent on development. Towards the end, the final build is completed and a demo is presented to the customer for feedback.
When choosing which functional requirements to deliver upon first in early iterations, the books recommend a combination of requirements based on Risk-Driven Development and Client-Driven Development. Risk-Driven Development recommends focusing on those high risk functional requirements that are very critical to the core of the architecture. Client-Driven Development focuses on those functional requirements perceived to be of high value to the customer. Delivering on these combinations will satisfy those needs important to you as a developer and those needs important to the customer.