Jethro, also known Reuel, was a Kenite priest of Midian and Moses' father-in-law by Zipporah. While only a few episodes of his life are documented in Scripture, he undoubtedly had a major influence on Moses' life. When Moses fled to Midian after killing an Egyptian, Jethro hired Moses as a farm hand and gave his daughter Zipporah to him in marriage. When Moses was called to Egypt, Zipporah and their sons Gershom and Eliezer were sent back to live with Jethro for a time. Later, Jethro came to visit Moses and the nomadic nation of Israel in the Sinai desert after hearing of the events of The Exodus. During his stay, Jethro advised Moses to delegate his judicial-mediator responsibilities to different people to lessen the caseload and create faster judgements for the people. His son Hobab joined the nation of Israel as a foreigner.
Reuel was born in Midian and was given his name, which means "friend of God". He would later become a priest of God. It is not known whether or not the priesthood was hereditary in Midian (thus his name) or if he became a priest on his own accords. Regardless it seems the nation of Midian worshipped God and Reuel would have been raised in Yahwism.
At one point Reuel acquired a flock of some sort. He also had seven daughters and one son. He tasked his seven daughters to care and feed his flock.
A Son in law
Once Reuel had his flock and his daughters were tending it, Moses came up to Midian as a refugee. Moses rested by the well that Reuel's daughters usually gathered water to feed his flock. When local shepherds began harassing the daughters Moses drove them off and watered Reuel's flock.
With their work done the daughters returned to their father. Reuel noticed they had returned from flock tending much earlier than usual. Reuel's daughters told him of the Egyptian who completed their work. After Midian's priest heard this he told his daughters to give hospitality and invite the man to eat with them. Once Reuel ate with Moses he offered him residence. Moses agreed and in time Reuel gave his daughter, Zipporah to him in marriage. Based on Zipporah being wed first she may have been the first born daughter. 
Reuel's son-in-law stayed with him forty years and bore him two grandsons during this time, Gershom and Eliezer. During the forty years Moses tended Reuel's flocks instead of or alongside his daughters.
After forty years Moses asked Jethro's permission to return to Egypt and permission was granted. Once Moses liberated the Hebrews from enslavement he sent his wife and sons back to Jethro who cared for them some time.
Advisor to Moses
After Israel had defeated the Amalekites in battle, Jethro heard of Moses' success. So Jethro went to go see his son-in-law, sent word ahead and brought his daughter and grandchildren along with him. He may have brought his son Hobab, explaining Hobab's involvement in Israel. After he greeted Moses at Mount Horeb, Moses told him everything that he had had experienced. Jethro rejoiced at the news of the liberation from Egypt and exclaimed that he now knew that God was greater than all other gods. This expression may have been just praise, but this could also indicate Jethro was doubting or beginning to worship other gods.
Then Jethro brought a burnt offering, sacrificed it and then ate at a banquet with the elders of Israel. The following day Jethro noticed Moses spending the entire day judging cases. Astonished, Jethro asked Moses why he was the sole judge of Israel. When he was told that only Moses knew the laws, Jethro began to advise Moses. Jethro suggested that all of Israel should be educated in the laws and taught how to live, which was a revolutionary idea for the world at the time. Jethro also told Moses to assign judges over different jurisdictions to more efficiently judge cases. Only the most undisputed cases would be judged by Moses after going through various other judges. Moses listened to his father's advice and after this Jethro was sent home.
The process of judge selection may have taken several weeks to months, so Jethro could have been an advisor for a long period of time.
While Jethro is minor in his textual descriptions he made several impacts on Israel and on Moses.
The name Jethro
While he is referred to as "Jethro" Scripturally this was likely not an actual name of his. The name Reuel which means "friend of God" is used less frequently than Jethro which means excellency. Since the name Reuel was a theonym and he lived in a nation that likely followed God it can be reasoned this was his name. While the name Jethro is used more frequently than Reuel it was always used in the context of him being Moses's father-in-law. Similarly Reuel is used only in reference to him prior to the text stating Moses's marriage to Zipporah (the exception to this is when Hobab is mentioned he is called "the son of Reuel".
Based on all of this it can be reasoned that Jethro was an epithet or a title of respect. Moses would have used the term "Excellency" to refer to his father-in-law out of respect. The name Reuel is used only before this is revealed, so Jethro may have been avoided before the reader knew he was Moses's father-in-law.