As it turns out, this person claims that she is actually a very prominent doctor in Nigeria. She was so kind and kept telling me how nice my voice was and how handsome I sounded. Tomorrow, we're going to arrange the return of several million dollars owed to her upon the death of her father. For some reason, we need to use my bank account though. Oh well, she says I can keep a small percentage for my troubles!
More seriously -
There actually have been people who fell for that scam.
In fact, some have traveled to Nigeria, to "claim boxes full of money".
-- Then, their relatives were notified that the visitors were incarcerated / held for ransom / etc.
Google "419 scam" for more info.