Agile method combines both incremental and iterative methodology. It is iterative because it plans for the work of one iteration to be improved upon in subsequent iterations. It is incremental because completed work is delivered throughout the project.

What are agile iterations?

An iteration, in the context of an Agile project, is a timebox during which development takes place, the duration of which: may vary from project to project, usually between 1 and 4 weeks.

How many iterations are in a sprint?

A sprint is normally an iteration. But you can for example have a 4 week sprint, but have 4 one week "internal" iterations within that sprint. There is a lot of discussion about the length of sprints. I think that if you do it according to the book they should all be the same length.