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It's a system like a local telephone system, where you dial up to a certain apartment and then they press a button that opens the door for you.

An intercom that lets someone at the gate talk to the apartment in question to try to convince them to buzz them in?

Yes. They press an apartment number which dials your phone. "Hey your pizza is here", then you press a button on your phone which opens the outer gate or the front door to the building. You then meet them at your front door.

It's like a phone for the yard door. Someone buzzes you, you talk to them and let them in or not.

The intercom would be for a guest to use to request access. See Seinfeld episodes for an example.