The white room was an environmental chamber through which technicians, support personnel, and crew members accessed the Command Module.

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Adapted from p. 1-2 (p. 8 in the PDF) of the Apollo/Saturn 5 - Launch Complex 39, Mobile Launcher Service Arms, Operations and Maintenance Technical Manual
Extraction and clean-up by heroicrelics.org.

The white room was mounted on the top-most swing arm on the rocket's umbilical tower. For Saturn V launches, this was swing arm 9 on the Launch Umbilical Tower (LUT). For LC-34 and LC-37, the Saturn IB pads, this swing arm was simply called the "Apollo Access Arm" on the Umbilical Tower (the Saturn IB towers had three swing arms, Swing Arm No. 1 through Swing Arm No. 3, to service the rocket plus the "Service Module Swing Arm Umbilical Disconnect" and the Apollo Access Arm to service the spacecraft).

I am aware of two surviving Apollo white rooms. One is displayed at the Kansas Cosmosphere and one is currently part of Kennedy Space Center's Ad Astra Per Aspera exhibit (this white room was formerly displayed outdoors).

Kennedy Space Center once had a photo archive which included several photos of the white room and swing arm #9.

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NASA photo KSC-66C-4981, showing swing arm #9 prior to the installation of the white room.

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NASA photo KSC-66C-4985, showing swing arm #9 after the installation of the white room.

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NASA photo KSC-66C-4983, showing the Command Module side of the white room.

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NASA photo KSC-66C-4984, showing the outboard side of the white room. I've always been curious about the door at the end, as it simply opens into the open, some 330 feet above the mobile launcher.