This is a secret passage to the Railroad HQ. The entrance is in the basement, at the end of the corridor. There, you find a turn dial with letters which you need to arrange into RAILROAD, confirm each of the letters with the button in the center.
You cannot enter the HQ until you join the faction, or you eliminate them. The headquarters is small and there are few interesting people:
Desdemona the faction leader. You receive the main quest from her,
You can have Dr Carrington treat your wounds and sell you some meds,
Tinker Tom is a merchant that later on, after you have made sufficient progress into Railroad quests, also gives you several well-paid ones,
Robot PAM tasks you with replayable quests, depending on your progress into quests,
On the table at the exit, there is an issue of Astoundingly Awesome Tales.