API stands for ‘Application Programming Interface’. It’s simply a software mechanism that allows two different systems to talk to each other and exchange specified bits of information.
A large proportion of the services and websites we all use online leverage APIs. For example, when you use a flight comparison website to book a flight, the comparison site searches all of the airline databases via an API to return matches to the search terms you entered.
Open banking APIs work in the same way. When Bud refreshes your transactions in the app, it's pulling the updated information from each bank using the bank's secure API.