What's the chemical nature of a dishwasher's rinsing agent?
According to the MSDS for Jet Dry (a common brand name) it contains:


Sodium 2-phenylpropane-2-sulfonate (Sodium cumene sulfonate) 
Propane-1,2-diol 
Citric acid


I think it may be safe to assume that the citric acid is in there for a "clean" smell and also to soften the water (thanks to the commenter).  The sulfonate is presumably a surfactant to help break the surface tension of the water, and promote evaporation, and the propylene glycol may help serve as a coolant (and is favored due to low toxicity).