While this question may seem obscure and unimportant, Alexius I’s action is actually quite important in Western history. This is because his request led to the First Crusade. Basically, Alexius I asked for military assistance because his empire was hard-pressed by the Seljuk Turks.
The Seljuk Turks were a central Asian people who took control of the Muslim Abbasid caliphate centered in Baghdad. By the late 1000s, they controlled that empire and had enough power to mount military campaigns against Egypt and against the Byzantine Empire in an attempt to expand their territory. In 1071, the routed the Byzantines at Manzikert (famous battle) in what is now Turkey.
Ten years later, Alexius came to the Byzantine throne. He inherited a weakened empire. It had been weakened by poor leadership and by religious tensions between the Catholics and the Eastern Orthodox within the empire. It was also threatened from the outside. One of these threats was from the Seljuks.
Upon taking power, Alexius defeated some of the external powers that were threatening his empire. However, he lacked the resources to truly fight the Seljuks, who were the greatest threat. Feeling that it was necessary to push back against the Seljuks, Alexius appealed to the West for help. This led to the calling of the First Crusade by Pope Urban II in 1095.