"Honor your father and your mother" (Exodus 20:12) is the fifth of the Ten Commandments. It is at the very heart of Judaism and is a mitzvah that straddles the twin aspects of Judaism: “bein adam la’makom” (between human and God) and "bein adam l’chavero” (between human and human). Honoring parents recognizes the process of creation and enables us to appreciate God’s role in the creation of life.
A lesser known mitzvah, however, is "Every person shall revere/fear his/her mother and his/her father" (Leviticus 19:3). To honor one’s parents requires providing for their personal needs (food, clothing, shelter, etc.). To revere/fear one’s parents is to make certain never to undermine their dignity (not contradicting one’s parents, not sitting in their specific seats, etc.)
Note that when the Torah speaks of reverence/fear of one’s parents, “mother” precedes the word “father,” yet "father" precedes "mother" when the Torah commands us to honor our parents. The word sequence reveals a strikingly accurate understanding of family dynamics. In many homes, the nurturing role of the mother makes her more beloved to her children than the father. It is easy to want to honor her, to take care of her. But, the Torah places the word “father” first, with respect to honor, as a reminder that the father deserves an equal measure of honor. So too, it is often the father, who may be more distant from child-rearing (and who is often the disciplinarian), who is naturally revered/feared by the child. The Torah, therefore, uses the word “mother” first, in order to uphold their equality with respect to fear/reverence. Hence, children must revere/fear and honor both their mother and father equally.