Why is preferred on the construction of big stadium roofs and of cooling towers, per example?
What is the advantage of this geometric figure that makes it more economical?
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Assuming that you mean a "Hyperbolic Paraboloid", the answer is that it's easy to make from common construction materials due to the fact that the surface can be made up of straight lines.
There are other reasons to choose a shape like this over e.g. a flat or pitched roof (aesthetics, drainage, etc.), but I take your question to mean "why choose this specific mathematical shape, rather than something else similar (that apparently ticks all the same boxes)?"