A Third Party Provider is any company who wants to offer you a service, and therefore needs your account information to do so. Third Party Providers are approved by the Financial Conduct Authority (FCA) before they can take part in Open Banking. All approved Third Parties will appear on the Open Banking Directory.
We don't know which companies will apply to become an authorised third party provider, but they could be other big high street banks, newer smaller banks, or other companies that aren't banks but provide similar services e.g. credit reference agencies, and comparison websites. Major retailers are also on the current list, including Argos, John Lewis and Amazon.