The Tempest Stronghold is the outpost of the Tempest Dragons. When Training Camp in this outpost is at level 10, you can train Tempest Cabals.
The buildings in this outpost will increase the stats of the Tempest Dragons, and the Tempest Cabals when they are marching with the Tempest Dragons.
To be able to build this outpost, you need the Tempest Dragon Eggs. It is one egg that contains both the Thunder Dragon and the Lightning Dragon. The only current way of getting the egg is from events like tournaments. You may need to build it on a mountain.