“our king may govern us.” The Hebrew word translated “govern” is shaphat (#08199 שָׁפַט), and its most basic meaning is “to judge.” Its meanings include “to judge, to decide between, to settle disputes, to administer justice, to rule, to be in authority, to govern.” In this context it has the meaning of “to govern” with likely an emphasis on settling disputes. The Israelites were prone to ungodly behavior, and no doubt the decisions rendered by the elders of any given town were political and ungodly. Sadly, having a king instead of local elders and tribal leaders would not remedy that. Throughout history, people have been willing to give up their freedom and personal responsibility for being governed by others.
“and go out before us and fight our battles.” The people wanted a warrior king, and they got Saul, who was apparently a valiant warrior. However, as we learn more and more about Saul we see that he was not a particularly godly man.