A trophy room was a room where trophies or relics were kept.
The Kazon and Hirogen kept trophy rooms aboard their ships. (VOY: "Initiations", "Hunters")
In an alternate timeline, General Jean-Luc Picard kept a trophy room in his house that contained displays of several weapons as well as various skulls of the general's enemies. Weapons displayed included a Zhat Vash dagger and disruptor rifle. Skulls displayed included the Borg Sentinel One of Two, the Ferengi Grand Nagus Zek, the Saurian Commodore Y'Shi, the Lihn Zhee Chieftain M'Talas, the Cardassian Gul Dukat, the Klingon General Martok, and the Vulcan Director Sarek. (PIC: "Penance")
Designer Neville Page provided the identification of the Saurian and Lihn Zhee skulls on Twitter. [1] [2], while Dave Blass previously provided further details on Instagram. [3](X)