Earlier quoted context omitted.
Language servers are local services that analyze the code outside of your editor (and can be used by several editors etc). It's a protocol that got big the last 2 years or so. It doesn't refer to servers in some Cloud.
So... daemons?
The IDE (in this case atom) spins up the process and shuts it down when necessary, and then both sides communicate to each other using an implementation-defined IPC mechanism.
So it's a server more in the sense that the IDE requests info as a client, and then the server provides it (pull, not push).