There's a good explanation of what this means on Wired [1]. Hopefully this means the end of financial planning apps asking for my online banking password. Interestingly they also suggest online payments might go directly through the bank rather than a payment provider like WorldPay, but I guess that depends on how varied the APIs are.
1: http://www.wired.co.uk/article/open-banking-cma-psd2-explain...