By showing us pictures of starving children, beaten up women, people struggling with cancer, and so on, these adverts are appealing to our emotions, in particular, emotions such as empathy and guilt. Put simply, these adverts work by arousing negative emotions in the viewer (emotions that the viewer will want to escape because they are unpleasant) and then offering the viewer a way to escape such emotions, i.e. by donating (Pratkanis, 2007). In this case, the image of the child might arouse feelings of empathy, which you can then escape by giving a donation to Action aid.
The idea that negative emotions, in particular, empathy, can lead to higher levels of helping behaviour has been consistently supported by research. For instance, Griffin, Babin, Attaway, and Darden (1993) presented participants with a written charitable appeal of a man who had lost his vision asking for donations to assist with his medical bills. They were then asked to rate their responses to the appeal for assistance, including their emotional reaction (empathy and personal distress) and their causal attributions (whether they attributed a high amount of responsibility to the man's actions or to less controllable factors). They were also asked to indicate the likelihood that they would (or would not) give, as well as the amount that they would be likely to give.
They found that the stronger the feelings of empathy were, the more likely they were to give. This suggests that empathy is instrumental in creating intentions to give charitable donations. They also found that participants who assigned high levels of responsibility for the blindness to the victim expressed lower intentions to give, compared to those who believed that it wasn't his fault. Figure 2 shows how these factors are related to giving intentions in a model. It shows that gender and distress have no significant effect on intentions, whilst empathy and attributions significantly effect giving intentions.
This research suggests that charity appeals often induce empathy in people, and that the more empathy someone feels towards a cause, the more likely they are to donate. It also suggests that people are more likely to donate if they think that the adverse circumstances facing those who the appeal is directed at are not at fault- this may explain why charity adverts try to communicate across the message that people are helpless to change their situations and it isn't their fault; i.e. that starving, being beaten, have cancer, etc. is not their fault
Griffin, M., Babin, B.J., Attaway, J.S., & Darden, W.R. (1993). Hey you, can ya spare some change? The case of empathy and personal distress as reactions to charitable appeals. Advances in Consumer Research, 20, 508-514.
Pratkanis, A. R. (Ed.). (2007). The science of social influence: advances and future progress. Frontiers of Social Psychology. Philadelphia, PA: Psychology Press.