25Now great crowds accompanied him, and he turned and said to them, 26"If anyone comes to me and does not hate his own father and mother and wife and children and brothers and sisters, yes, and even his own life, he cannot be my disciple. 27Whoever does not bear his own cross and come after me cannot be my disciple." 
—Luke 14:25-27 

We learn in Luke 14:25 that anything less than total 100% radical commitment to Christ is not commitment at all. Jesus said, "If you don't hate all other human relationships compared to your relationship with Me, you cannot be My disciple."

You ask, "What does He mean by hate my father and mother?"  In Matthew 10:37, He said it a different way: "Whoever loves father or mother more than me is not worthy of me, and whoever loves son or daughter more than me is not worthy of me." Now that is what commitment is—to Christ first, above everything: my wife, my children, everything.  Most parents know it's a struggle not to love their kids more than they love God. You are not helping your kids at all if you love them more than you love God. 

That's the whole point of the story of Abraham and Isaac. God told Abraham, "You can't love anyone or anything more than Me. So get your son and take him up on the mountain and offer him on an altar there" (See Genesis 22:1-19). The great test was on.

A couple of years ago when my family and I were on sabbatical, I was wrestling with this exact issue. I came to a decision. I took my sons to the top of a high hill in northern England. Sheep were everywhere—a beautiful setting.  I read to them the story of Abraham and Isaac. I communicated to each of them, "Son, I can never love you more than I love God."  We knelt down and I laid my hands on them and consecrated myself and them before the Lord to always love God first. 

Now when you have settled your commitment to Christ, then comes the same level of commitment to your family. Anything less than total 100% radical commitment to my wife, to my husband, to my children, to my parents is not commitment at all.

You say, "I don't know if I have that kind of a commitment to my family."  Well then you need to repent and ask God for forgiveness and start over. You will love your children better when you love God first.  (For much more on this see my book Seven Words to Change Your Family (Moody). —James MacDonald