Who has the power in a constitutional monarchy depends on the structure laid out in the constitution. Although this political system includes a monarch as the head of state, the monarch's powers are not absolute.
A constitutional monarchy relies on a strict set of parameters detailing how the government functions and what role the monarch serves. These parameters are often formally codified in a written document, although unwritten forms exist, as is the case with Great Britain.
In many constitutional monarchies, the monarch must work in tandem with a democratic parliament to make decisions. Some decisions may not involve the monarch at all. This system ensures a balance of power that keeps the monarch in check.