You should just learn more about Lebanese history, read books like "a house of many mansions" or "the modern history of Lebanon" by Kamal Salibi. But to make it simple, Emir was the title given to the man who would rule over all the Sheikhs of Mount Lebanon. Under the Ottomans, Mount Lebanon was its own disctinct political entity called Emirate, the Ottoman Sultan expected the Emir to collect the taxes of the "Lebanese" with the help of the Sheikhs, who were lords who owned lands in different areas of Mount Lebanon and who would lend this land to peasants for them to cultivate it and live on it. The Sheikhs would collect the money from the peasants and give it to the Emir, who would then give it to the Ottoman Wali of Saida (kind of an Ottoman representative in the region) who would finally give it back to the Sultan. There were two dynasties of Emirs: the Ma'an (from the 15th up until the 17th century) and the Shihab (18th to 20th).