localhost
The address a machine uses to talk to itself. `127.0.0.1`, and `localhost` is the name for it. A local model runner listens there, so `http://127.0.0.1:1234` reaches LM Studio on the machine you typed it on and nowhere else. Nothing sent to it leaves the computer or touches a network.
The number after the colon is the port, which is how one machine keeps several listeners apart. LM Studio takes 1234 by default, Ollama takes 11434, and if something else already holds the port you pick a different one and change it everywhere you wrote it down.
Reaching the same server from your phone or a second laptop is a separate decision, and every runner makes you go and turn it on. That is worth knowing before you assume it is off: the moment a model answers on your LAN address rather than the loopback one, anything on the same wifi can send it requests, and there is no password in front of it by default.