server
A server is a program that waits for calls and answers them, running on a machine with nobody sitting at it.
In more detail
The word names a program, not the machine it runs on. One machine may run the program that answers for a website, the one that answers for a database and the one that creates PDFs: three servers, three programs, one machine.
What matters about one is that it is always there and always answers the same way. That is why it is asked, once in a while, whether it is up — a call that does nothing but come back.
What it does on a real document
The one that creates PDFs holds the engine and nothing else. It takes a description, writes the pages, hands them back and forgets the lot; it keeps no copy of what it created.
It can run on our machines, which is what the service is, or on yours, which is what the licence covers. The call your program makes is the same call either way — only the address changes.
Where it comes from, and why
The idea is older than the network: one machine doing work several others ask for, so that the work is done once and well rather than everywhere and badly.
What changed is where it sits. A machine in a cupboard down the corridor and a machine in a data centre answer the same way, which is why moving between the two is a matter of changing an address.