"Temporal Observatory" was a term used by Temporal Agent Daniels to describe a holographic representation of the time stream. It allowed Daniels and other temporal agents to supervise various activities being carried out by time travelers. The display was projected by a space-time scanner.
Daniels showed Captain Jonathan Archer a Temporal Observatory in 2151, hoping it might make Daniels' reality clear to Archer. Upon viewing the display, the captain felt extremely overwhelmed. Daniels used the presentation to point out the time period he himself originated from nearly 900 years in the future (the 31st century), as well as an earlier century where the Suliban Cabal's mysterious benefactors were, and a group of anthropologists in 2769.
When Archer told Commander Charles Tucker III about having witnessed the Temporal Observatory, Tucker likened it to an experience he had in a highly realistic holographic chamber on board a Xyrillian starship. (ENT: "Cold Front")