An API (application programming interface) is the standardised way programs talk to each other: a set of rules that lets one application fetch data from or delegate operations to another system.
An API is like a waiter between the dining room and the kitchen: the application places an order ("give me the product list"), the system on the other side fulfils it and returns the result. Through APIs a store connects to a payment provider, an app to maps, a website to a CRM – without knowing their internals.
In product design the API determines flexibility: a well-designed one lets you connect a website today, a mobile app tomorrow and a partner integration next month – all to the same data.
For buyers: ask "does it have an API?" about every system you purchase. No API means manual data re-entry and lock-in to a single vendor.