The question is in two parts - one about judging and the second about all that a "judge" does.
The operative Hebrew word is "shaphat" and the cognate root of the words used to describe what the "judges" did in the Bible book called Judges. Young says this word means to act as a magistrate. While this is true, it had very loud overtones of what we would today simply call governing. The verb is used regularly:
- Judges 3:10 - Othniel judged Israel
- Judges 4:4 - Deborah judged
- Judges 10:2 - Abimelech judged Israel 23 years
- Judges 10:3 - Jair judged Israel 22 years
- Judges 12:7 - Jephthah judged Israel 6 years
- Judges 15:20 - Samson Judges Israel 20 years
The function of these judges was more than just to decide disputes; it was to provide general leadership and particularly act as a military leader, God's appointed agent, to reform Israel and their constant backsliding and deliver from the hands of whoever was oppressing them at the time. All judges did this and once appointed served until their death.
After the death of each judge, Israel would rebel and turn to other gods, often the Baals, and God would appoint another judge to reform and deliver Israel. This was often done, as in the case of Abimelech, Jephthah, Gideon and Samson (at least) among their many notorious exploits and acts of heroism and sometimes rash stupidity. Despite their human frailties, God still used them to keep reforming Israel to turn the people's hearts back to him.
The last two Judges, Eli and Samuel about whose lives we know much more, were just as human and made very serious mistakes in some areas. For example, they did not rebuke their way-would sons adequately and both had very disappointing children. Nevertheless, they judged Israel for an extended time.