The Scholars possess great knowledge and intelligence of the outer worlds beyond their kingdom. They have devoted their entire life to studying the ancient times of combative and military tactics. By summoning the information they have in mind, they are able to aid the army on neighboring city conquests and control their citizens with their philosophical clutches.
Strictly speaking, Scholars are not "siege" units. They are in a category of their own. However, because of their close association with attacking cities, they are included in the category here. Scholar units are recruited/trained in the Academy instead of the Workshop.
The Scholar will decrease the amount of loyalty the enemies' city has. Once loyalty falls to 0 in a city, it is considered conquered and the scholar is assimilated into that city. Typically, it would take multiple waves of attacks to conquer a city, because the amount of Scholars sent per wave does not matter. Each Scholar's cost in resources will increase depending how many conquered cities you possess, as well as each Scholar that is available in production.