I just read on the internet that some people believe bananas can cure depression. Researchers point out that the myth is exaggerated, but some nutrients in bananas are known to be able to "help fight against depressive symptoms."
According to this article, bananas provide tryptophan, an amino acid that helps bodies make serotonin; serotonin is known for regulating our mood, and people with depression tend to lack serotonin. Also, a common symptom of depression is insomnia, and tryptophan can help people fall asleep more easily. Other than tryptophan, bananas provide vitamin B6, which also helps makes serotonin; vitamin B6 doesn't necessarily cure or prevent depression, but a healthy intake of it can decrease the risk of depression, especially as you grow older. Another article says that bananas also contain dopamine, which regulates our mood, ability to concentrate, and emotional stability.
Although bananas contain these "nutrients," researchers say they are only in very small amounts, and that almost all protein-based foods provide trypophan. Therefore, bananas do not provide a "unique or particularly significant source," they just contain nutrients that can somehow be connected to our mood, etc.
I personally don't like bananas anyway, so I'm sticking with the "an apple a day keeps the doctor away" saying :p