API key
An API key is a long secret string your program sends with each call, so that the service knows the call is yours.
What the word means
A person signs in with a name and a password. A program cannot: there is nobody at the keyboard to type them, and leaving a password inside a program would be worse than useless.
The key does the same job in one piece. It is long enough that nobody guesses it, it belongs to one account, and it can be replaced without touching the account it belongs to.
What it does on a real document
Every call to the rendering service carries the key, and what is counted against your plan is counted against it. It is also how the service knows which typefaces you uploaded and which belong to somebody else.
It is never shown again on a page after it is created. If somebody else has seen it, the answer is to make another and delete the old one; nothing else has to change.
Where it comes from, and why
The habit grew with services called by programs rather than by people. A password belongs to a person and unlocks everything; a key belongs to one program and can be taken away on its own.
It is the simplest of several ways of doing this, and the one that asks least of the program calling. That simplicity is also its weakness: whoever holds the string is you, so it lives in the settings of your server and never in a page or a message.