The Crystal Palace is a location where the final Star Spirit is being held during the events of Paper Mario. This palace is a 'mirror' filled castle with puzzles in every which way. Mario and his teammates must solve the puzzles and fight off many Duplighosts and White Clubbas to get to the boss. After solving the puzzles, they manage to reach the Crystal King. After they defeat him, they free the last Star Spirit, Kalmar.
Comically, at one point in the palace, four Duplighosts pretend to be Kooper and say they are him, when in actuality they turned into Goompa, Kolorado, Koopa Koot, and Luigi, and act like them (with the Luigi one even calling Mario "Brother").
Many of the walls look like mirrors, but they're actually just glass, because the reflections are always Duplighosts in disguise. The palace has two areas, the front (main) area and the rooms behind the glass walls. Each will need to be inspected carefully, because going back and forth between them can be confusing, since they're almost exactly the same.
The Crystal Palace was once a shrine to the Star Spirits, but its location and how to get there became lost over time. The only way to reach it is a secret passage in Shiver Snowfield to Shiver Mountain, where at the top is the palace.
In Paper Mario: The Thousand-Year Door, Koopook mentions in his RDM to Mario that he is hiding in a place called the Goomstar Temple. This is actually a mistranslation of the Crystal Palace's Japanese name (Kurisutā Shinden) and Goomba (Kuribō). All other languages call the Crystal Palace by its real name.
Several items can be dropped by enemies found in this area. Items found in the overworld include:
In-game map description
Names in other languages