You are actually referring to one of the Ten Commandments, which were given by God to provide us with a moral and spiritual foundation for our lives. One of the commandments says, "Honor your father and your mother... that it may go well with you" (Deuteronomy 5:16).
To honor someone means to treat them with respect -- not necessarily because they are perfect, but because God has given them a unique place in your life. You only have one father and mother, and in spite of their faults, God gave them to you -- and He gave you to them. No one else (except your siblings) has this relationship with them, and you should respect them because of it.
Pray for your parents; prayer is one of the best ways to honor them. In addition, do what you can to hold the door open to reconciliation. Don't hold on to resentment, anger or bitterness; they'll only hurt you. If you need to seek forgiveness for anything you did wrong, do so. The Bible says, "If it is possible, as far as it depends on you, live at peace with everyone" (Romans 12:18).
Does this mean you overlook their faults or pretend your parents are different than they really are? No, of course not. But it does mean you do everything you can to let them know you are thankful they brought you into the world, and you care what happens to them. Thanksgiving would be a good time to express this.