On projects which follow a waterfall methodology and run into project delays, usually there is nothing to demonstrate to the client. This is a little different with iterative and incremental methodologies. Iterative meaning we repeat the life cycle processes over and over, with an incremental addition in each run. With iterative and incremental development a delayed project can demonstrate an artifact to the client. It might not be everything the client wished for, but it is there.
Iterative and incremental methodologies provide higher levels of confidence to project sponsors, who would be more willing to extend investment in a troubled project than a project with no output at all.
Agile methodologies embed iterative and incremental approaches. Examples are Rational Unified Process (RUP), SCRUM, XP and others.
Great leaders know how to scope these increments and how often should they come out. For example lets consider a generic problem well know to everyone, the current economy down fall. This problem does not have a one shot solution. A $700 billion stimulus plan will not solve it for once and for all. It is just an iteration that will yield some results in 18-24 months, to keep things afloat. Most probably another iteration will be needed to sustain some of the new initiatives started in increment 1, and so on.
We apply iteration and increment processes in our daily lives as well. When we go to the grocery store to purchase soup, we don't purchase 100 cans of soup for the full year, even if we could successfully store them and pay for them. We purchase maybe 5 or 10 cans for a week or two, we then repeat the grocery purchasing process in one or two weeks.
Reasons for iteration are many,
(a) gain confidence in an experience to decide whether to repeat it or sustain it or not
(b) streamline cash flow
(d) effective time utilization
(e) limitation in resources
(f) shorter demand cycles (time to market, constituent demand, etc..)
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