The meaning is: Be a righteous role model for your children. Be a righteous good person so that your children and others would follow your example. It is impossible for children to raise up for high morals and sublime principles even if they hear hundreds of advices and guidelines while they are watching their parents do against these advices.
Some fathers are not good models for their children. They show bad manners with their children, wives, and people as well. For example,
1- They have lewd tongues while they want their children with clean tongues and of good speech to the extent that once I saw one of my relatives when his son entered and slandered him, and the father kept laughing as if nothing happened. Furthermore, the father said: See how my child grow up.
2- When a father at home and the phone rings, he says to their children, tell them: “I am not home,” and a child will be in a chaos. The Prophet (peace be upon him) explains to us the danger of this action. `Abdullah ibn `Amir (may Allah be pleased with him) narrated: “My mother called me one day when the Messenger of Allah (peace be upon him) was sitting in our house. She said: Come here and I shall give you something. The Messenger of Allah (peace be upon him) asked her: What did you intend to give him? She replied: I intended to give him some dates. The Messenger of Allah (peace be upon him) said: If you were not to give him anything, a lie would be recorded against you.”[1]
Some people think that children do not understand, so if the father lies to them, it will not be important, however, the truth is different. Therefore, an educator should realize that children have perception and feelings, and have emotions that he must care for and appreciate as should so that rearing would be fruitful.
3- He smokes before his children without paying attention or caring, not to mention its prohibition, it is also a bad behavior because the child shall be a smoker too, following the example of his father.
One of the smokers said: I have a four-years-old child. I left cigarettes on bed and went to pray Al Fajr then I came back to sleep. I woke up at the voice of my wife saying: Wake up and see what your son is doing in the kitchen? He continued: 
I saw my son lit the cigarette and put it in his mouth, and once the father saw the child, he was stunned but could gather himself up. He said: O child, why have you done this? He replied: I do as you do, father. It was a painful slap to the father and one of the reasons for quitting smoking.
How beautiful that children see their parents as good examples in the house, embodying the Islamic manners as live behavior, and children would feel and live that, leaving a positive effect in their souls.
The righteousness of the father affects his children, have not you read Allah’s Saying: “And their
father was a righteous man.” [Surat Al Kahf: 82].
Sa`id ibn Jubayr reported on the authority of Ibn `Abbas (may Allah be pleased with him): they were guarded by the righteousness of their father without mentioning their righteousness.[2]
Allah (Glorified and Exalted be He) did not mention the righteousness of the children, but mentioned the righteousness of the father, so the treasure was guarded by the righteousness of the father.
References:
1- Kayfa Turabby Waladaka Al Muslim, Shuqir Al `Itiby.
2- Al Wasa’il Al `Ilmiyyah Fi Tarbiyat Al Awlad, `Abdul-Majid Al Jumu`ah.
3- Kayfa Yurabby Al Muslim Waladah, Muhammad Sa`id Mawlawy.
4- Kayfa Tughayyir Suluk Tiflak, Muhammad Dimas.
5- Min Akhta’ina Fi Tarbiyat Awladina, Dr. Muhammad ibn `Abdullah As-Sihim.
6- Ifham Tiflak Tanjah Fi Tarbiyatih, `Adil Fathy `Abdullah.
7- Tarbiyat Al Awlad Fi Al Islam, Dr. `Abdullah Nasih `Ulwan.
