The female cicada killer stings the cicada and brings it back for lunch. She may go out for more because she is larger than the male. The dead cicada also supplies nutrients for the eggs laid by the female and male cicada killer. So unless you are from Malaysia or the Congo where cicadas are a prized treat, we can let the eastern cicada killer wasp do its work without fear that we will be stung by one of the largest wasps in the eastern United States. Check out the excerpt below from Wikipedia regarding the threat to humans.
"Although cicada killers are large, female cicada killer wasps are not aggressive and rarely sting unless they are grasped roughly, stepped upon with bare feet, or caught in clothing, etc. One author who has been stung indicates that, for him, the stings are not much more than a "pinprick". Males aggressively defend their perching areas on nesting sites against rival males but they have no sting. Although they appear to attack anything that moves near their territories, male cicada killers are actually investigating anything that might be a female cicada killer ready to mate. Such close inspection appears to many people to be an attack, but male and female cicada killers do not land on people and attempt to sting. If handled roughly, females will sting, and males will jab with a sharp spine on the tip of their abdomen. Both sexes are well equipped to bite, as they have large jaws; however, they do not appear to grasp human skin and bite. They are generally non-aggressive towards humans and usually fly away when swatted at, instead of attacking"
Cicada Killers on Wikipedia