It is the boy's mother who says these words to her son when he comes back to the cabin, having been unable to find Sounder. She says,

"Sounder might come home again.  But you must learn to lose, child.  The Lord teaches the old to lose.  The young don't know how to learn it.  Some people is born to keep.  Some is born to lose.  We was born to lose, I reckon.  But Sounder might come back" (Chapter 4).

When she says "you must learn to lose", the mother means that the boy must learn to accept when things do not go the way he wants.  In an immediate sense, she is telling him that he may or may not find Sounder, but whether he does or not, he must endure, either way.  In a larger sense, the mother is talking about the reality of their lives as poor black sharecroppers in the Southern United States in the later 1800s or early 1900s.  Struggling to eke a meager living off the land, families like the boy's are in an impossible situation, victimized by prejudice, poverty, and ignorance.  Oppressed by laws that keep them down because of the color of their skin and unable secure even the basics for existence, they live life day to day, just struggling to stay above water.  The older ones have learned to suppress their longings for a better life in this world and in their powerlessness simply do the only thing they can do - accept life as it comes.  It is this lesson that the mother tells her son he must learn.

What is the significance of the quote "but you must learn to lose, son" in "Sounder"?

This is an important quote for a couple of different reasons.  The young (unnamed) boy who is the main character is growing up in the south where racism and violence is very common.  The boy must learn that no matter what he does, he will not be able to win against the mistreatment of the blacks.  If he "learns to lose" then he can move on and build from that.  The boy is able to use that by going out and learning how to read.  He becomes educated so he can provide for his family.  He then comes back home to work the land for his family. 

This boy is very unselfish and personifies that quote.  But he doesn't let racism rule.  He confronts it with courage and he shows the reader how to survive when it doesn't appear that survival is an option.  He will face a lifetime of loss with an unfair life, but if he learns to lose, he can survive.