The Fourth Commandment is: Honor thy father and mother; and it is distinguished from the other Commandments in being the only one that adds a definite promise of temporal blessing; "that thou mayst be long lived upon the land, which the Lord thy God will give thee."
     
The duties of children are to love, honor and obey their parents. In the Book of Ecclesiastes we read these beautiful words: "He that honoreth his mother is as one that layeth up a treasure. He that honoreth his father shall have joy in his own children, and in the day of his prayer he shall be heard."  (Eccles. 3:5-6.)  Sins against the Fourth Commandment are contempt, ill-will, and disobedience towards parents or those placed over us. Sins of this kind can be mortal or venial according to the matter. As is the case in the relations between God and His creatures, so in a lesser degree it is, with us and those whom God has placed in authority over us: Disobedience of children takes its rise from the vices of pride and selfishness. Obedience on the other hand is grounded on the virtues of humility and love. 
     
Humility
is shown in due submission to the parents, and respect for their natural position as heads of the family; and in the respect due to their age and years of experience. Love is the foundation of obedience; because the child should be ready to repay by devoted and loving obedience, the great debt that it owes to its parents, who have cherished and guarded it from its tenderest years.

DUTIES OF PARENTS
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Parents also have their duties towards their children. The chief of these are to provide for them; to instruct them in Catholic doctrine; to send them to Catholic schools; and by good example and every means in their power to bring them to God. As the soul is of much greater value than the body, and with it eternal issues are at stake, the obligation of having the children properly instructed in their religion is of far greater weight than that which concerns their temporal welfare.
     
The Fourth Commandment binds us to obey all justly constituted authority, and hence it binds us as citizens to obey all just laws of justly constituted civil authority. Christ tells us: "Render to Caesar the things that are Caesar's." St. Paul exhorts us: "Let every soul be subject to the higher powers: for there is no power but from God." (Rom. 8:  1.) Therefore the Church in educating her children as good Christians is also doing a service to the Sate in educating loyal subjects and obedient citizens.
                                                                     
REASONS WE SHOULD LOVE OUR PARENTS.  (St Thomas Aquinas)
Their union with us. Among those whom we are bound to do good are those in some way united to us. Thus, "if any man have not care of his own and especially of those of his house, he hath denied the faith," (1: Tim. 5:8.) Now amongst all our relatives there are none closer than our father and mother. "We ought to love God first," says St. Ambrose, "then our father and mother." hence, God has given us the Commandment: Honor thy father and thy mother."

The Philosopher (Aristotle was known as "The Philosopher") also gives another reason for this honor to parents, in that we cannot make an equal return to our parents for the great benefits they have granted to us. Therefore, an offended parent has the right to send his son away, but the son has no such right.
     
Since we owe our birth to our parents, we ought to honor them more than any other superiors, because from those others we receive only temporal things: "He that feareth the Lord honoreth his parents and will serve them as his masters that brought him into the world. Honor thy father in work and word and all patience, that a blessing may come upon thee from him." Ecclus. 3:8-10.) In doing this you shall also honor yourself because the glory of a man is from honor of his father, and a father without honor is the disgrace of his son." Ecclus. 3:13.)
      
Since we received nourishment from our parents in our childhood, we must support them in their old age: "Son, support the old age of thy father and grieve him not in his life. And if his understanding fail, have patience with him and despise him not when thou art in thy strength....Of what evil fame is he that forsaketh his father! And he is cursed of God that angereth his mother." (Ecclus. 3:14-15.) "With what measure you measure, it shall be measured to you again." (Matt. 7:2.) (St. Thomas Aquinas.)

Sources:  Rev. W. Frean, C.SS.R.- Commentary on the Catechism.
  St. Thomas Aquinas- God's greatest gifts.