What approach did you take to describe the benefits of SCRUM to clients / business units who do not have a technical background? Please list any analogies you thought were useful. Finally, how did you address the concerns that the Waterfall camp had?
I basically go around about risk reduction and ROI, since these are the main things people at the higher management level care about.
Using a incremental process significantly reduces the risk of wasting money on something that's not gonna be useful, because the customer helps steer the product development in the right direction through series of planned feedback cycles. The #1 reason for project failure according to the CHAOS research is lack of customer involvement. So why not use a process that eliminates that risk?
Also, with a incremental process you start delivering something in a much shorter time than when using a waterfall approach, which effectively increases the ROI (return on investment), since the customer starts benefiting from the product after one or two months, instead of waiting 6 to 12 months in a typical waterfall project.
You can also mention improved customer satisfaction, team self-improvement and self-management, which reduces the administrative overhead, improved employee satisfaction.