Since you have asked this in the business section, I will give an example from the field of business. The basic idea here is that this tactic involves trying to use logic and rationality to persuade someone rather than doing something like trying to use emotional persuasion.
So, for example, imagine you were doing a presentation to your bosses, trying to persuade them to make a change in your firm's processes. You would provide statistics about the problems that you think the firm has and you would then give a logical explanation of how your solution would solve those problems. This would be an example of persuading through rationality rather than emotion.