Let’s first have a look at what banks actually do.
cash & ATMs
FinTech services that are better / cheaper than the bank’s services:
cash, ATM: replaced by Paypal money transfers and by credit card companies (also through Apple Pay, Google Wallet, etc)
lending & insurance: http://techcrunch.com/2015/08/05/insurance-is-the-next-frontier-for-fintech/