The classroom is used to train a dweller's Intelligence. The room requires 30 dwellers to unlock. You can place up to 3 classrooms next to each other horizontally to increase size and number of assignable dwellers to this room.
A level Three classroom, called an Academy, will occasionally have the lights shut off for administration of the G.O.A.T. Examination. This is not a glitch in your power grid, and does not pose any risk to the vault.