The people of Israel did not like the way that Samuels son's chose to rule over them so they chose to send the elders in to talk with samuel about appointing a king. The children of israel wanted to be strong and organized like other nations in their minds.
Just as now we have a government that organizes our system and the president just like the king in the past is the great ruler who makes all the major decisions. They wanted a leader to govern them and make decisions in future battles.