The Arabic word Harem derives its original spelling and meaning from the Egyptian word harim, meaning ‘women’. In Egypt, A harem was simply the place where women lived. Any middle class home would have a harem, or women's room, where unmarried female relatives and servants would sleep. One would expect the king's palace to have similar facilities. There was, of course, a difference. The king had several palaces and so he needed several harems. It took a very large number of people to keep each palace functioning smoothly and so we would expect appropriately large harems. Even a half dozen women in the harem of a private residence could easily be integrated into the social and economic system of the rest of the house, but royal harems were so large that they took on a life of their own. Each harem needed its own estate, consisting of land and peasants to produce food for everyone and enough of a surplus to pay for all of the other necessities. Such a system would require its own officials and administrators, male of course, to keep everything running smoothly, but there is no evidence to suggest and no reason to believe that any of these men were eunuchs.
With the advent of Islam, and then the Turks, certain things changed. Under Islamic law, a man can have as many wives as he can support, with the traditional number topping out at around four. However, concubines were unlimited and many harems grew into the thousands. Historically, the concubine was frequently voluntary (by the woman and/or her family's arrangement), as it provided a measure of economic security for the woman involved. The Sultan's favorites, and the rest of his concubines main function was to entertain the Sultan in the bedchamber.
An Odalisque was not a concubine of the harem, Odalisques were ranked at the bottom of the social stratification of a harem, serving not the sultan, but rather, his concubines and wives as personal chambermaids. Odalisques were usually slaves given as gifts to the sultan, although some Georgian and Caucasian families urged their daughters to enter a harem as an odalisque, hoping that they might become a palace concubine, favored slave, or wife of the sultan. Generally, an odalisque was never seen by the sultan, but instead remained under the direct supervision of his mother or chief Wife. If an odalisque was of extraordinary beauty or had exceptional talents in dancing or singing, she would be trained as a possible concubine. If selected, an odalisque trained as a concubine would serve the sultan sexually, and only after such sexual contact would she change in status, becoming thenceforth a concubine. In the Ottoman Empire, concubines encountered the sultan only once—unless she was especially skilled in dance, singing, or the sexual arts, and thus gained his attention. If a concubine's contact with the sultan resulted in the birth of a son, she would become one of his wives.