The Weyrs are the Dragon settlements that act as homes, fortresses, hatcheries, and armouries. Not all Dragons are part of the Weyr factions, and "the Weyrs" is a phrase often used to refer to the dragons of the Weyrs as well.
Weyrs are very variable. Most are built into mountains or caves, large enough to contain dragons within. They tend to be complex, with many chambers, as well as great halls, armouries, and other functional rooms.
Most have magical protection also, in the form of powerful wards and barriers many centuries old.
Each Weyr has a Weyrlord, chosen by the Elders from amongst the dragon population. This individual is effectively in control.
There is also at least one Elder per Weyr, who uses magical communication to correspond with the Elders of other Weyrs. Together, they form the Council of Elders, which guides and chooses the Weyrlords. It acts as the final authority for the Weyr Dragons.
Some notable Weyrs. Only a few dozen survive overrall.