Prerequisites: Rally Point Level 15
At the tournament square your troops can train their stamina. The further the building is upgraded the faster your troops will travel over longer distances (effect takes place after a distance of 20 squares).
It only affects troops which were trained in the village where the tournament square was built.
The level dependent attributes (such as construction costs, generated culture points and troop speed) can be found here.
For the full table of construction times click this link for server with 1x speed and this link for server with 3x speed.