잘 - well/good/thoroughly/readily
나아요 - to get well/recover
Per the tips and hints in this skill, in Korea a disease recovers from you so 그 병은 나아요 is basically saying "regarding that disease, one recovers" (i.e. the disease can recover from someone). In English we would say either "that disease is curable/cured" or "one can recover from that disease".
Hence, 그 병은 잘 나아요 is basically saying "regarding that disease, one well recovers" (i.e. the disease can recover from you easily). In English this would be either "one can recover from that disease easily" or "that disease is easily curable/cured".
Hope that helps somebody.
I just tried "That illness is easily cured" and was marked wrong. I reported it, then came here. I think it definitely should be an option, especially as it was introduced to us as illness in a different part of the very same lesson. I think it is just an oversight; they only know what needs fixing if it is reported. All the best :)