Off of the dark, rainy node, the one with the owl's head that follows you. The map marks a secret on this node, and a grayed-out child node. Are they two different secrets?
There are two "secrets": the four owl puzzle (denoted by a question mark on the node), and the subsequent anticube room.
In four places, an owl appears at night. Speak with each one:
in the waterfall level near the pillar (green tree, first warp zone),
in the windmill level near the windmill (orange tree, air warp zone),
in the forest near the transforming cabin (green tree, outside rainy warp zone),
and outside the octopus-looking building containing the revolving model of the solar system and the counting cube (pink tree, temple/science warp zone).
These locations were shown on the walls of the fez-wearing elder's house (in Gomez's hometown, across the bridge).
After speaking with each owl, they fly to the rainy warp zone's giant owl room. When all four arrive, a panel reveals a door behind the owl statue opposite the entrance. It leads to another owl room with an anticube.
Glitch: If you remove the patch, the original version of the game had a glitch where you could access the hidden room without the four owls: stand in front of the entrance, rotate the room twice, and press up to enter. Keep in mind, the room won't be "completed" until the main secret (four owls) is finished and the next room is visited.