Turbotax asked me do I have an international bank account, is it asking that to know which bank to deposit my money into? What is the reason for the question?

TurboTax asks you about a foreign financial account because this is a reporting requirement of the IRS. People with foreign bank accounts have to report the fact on their tax return.

And if these accounts have balances over $10,000 at anytime during the year, they have a file a FBAR (Foreign Bank account report)