One of the key aspects of finite element analysis is the dimension of the elements. We can use the diameter of the sphere that circumscribes the element (if the dominion has three dimensions, the diameter of the circle that circumscribes the element if the dominion has two dimensions)to define the dimension of the elements.
Smaller is h more accurate is the solution of the problem. An accurate solution costs very much, in terms of computational time.
The optimal choice for h depends on the solution of the problem, e.g. if there is an area characterized by small gradients of the solution we can use a coarse mesh, so it varies locally. The optimal mesh is an unknown of the problem.