In skyrim, what do the paragons do?

In Elder Scrolls V: Skyrim paragons are used to teleport to a place in the Vale to find Elven weaponry and armor, jewelry, chests, magic scrolls and one of the Unknown Books.

There are 5 altogether:

The Amethyst Paragon is on a Frost Giant in the Forgotten Vale.
The Ruby Paragon is in the Inner Sanctum in a chest.
The Sapphire Paragon is on a Frost Giant across the river from the Paragon Platform.
The Emerald Paragon is on the Path of Resolution.
The Diamond Paragon is found near the Path of Radiance.

The Diamond and Emerald Paragons can also be found on Frost Giants in the Forgotten Vale.

Once a Paragon is obtained go to the Paragon Platform and insert the Paragon into the socket. A portal will appear between the columns allowing you to transport to a place in the Vale.