An API, or Application Programming Interface, is an interface between different computer programs. Basically, the API is how different software, or different parts of a software, speak to each other. The API is the set of rules that determine how the different parts interact. Think of it like a cable that connects two electronic devices. The cable that connects a computer to a power outlet allows electricity to flow into the computer, which interacts completely different from the cable from the computer to a pair of headphones or a USB cable connecting the computer and a smartphone. By plugging in a certain cable to the computer, you are telling the computer how to interact with the other device.
Someone who holds crypto will come in contact with the term API when they connect with their exchange in order to acquire information, such as documentation needed to file taxes. Using an API key, a customer can download transaction information such as when purchases, sells, and transfers were made and the price of the cryptocurrency at the time of the transaction.