Laban had cheated Jacob several times. Originally Jacob had agreed to work 7 years for Laban, and his wages would be to marry his youngest daughter, Rachel. After 7 years, Laban deceived Jacob by bringing to him his eldest daughter Leah to take in as his wife during the night. In the morning he saw that it was not Rachel, and Laban told Jacob that he would have to work another 7 years for the hand of Rachel. (Thus cheating Jacob of his first 7 years wages).
Jacob worked the additional 7 years and took Rachel as his wife. He continued to work for Laban as Leah and Rachel bore children. Finally, Jacob wanted to leave and go to his own country, and Laban begged Jacob to stay, because Laban had prospered because of Jacob.
Laban asked Jacob to name is wages. Keep in mind, according to Genesis 31:7, Laban had deceitfully changed Jacobs wages 10 times, yet Jacob stayed and worked faithfully for Laban. There had been habitual deception and cheating toward Jacob while Laban prospered at the expense of Jacob.
Jacob stated that when he came to Laban, Labans flock was very few, but it prospered under the care of Jacob and grew to a good size. Jacob continues to state in Genesis 30:32 Let me pass through all your flock today, removing from there all the speckled and spotted sheep, and all the brown ones among the lambs, and the spotted and speckled among the goats; and these shall be my wages.
According to the New Commentary on the Whole Bible it provides the following insight regarding Jacobs request:
Eastern sheep were generally white, and the goats black; spotted or speckled animals were comparatively few and rare. Jacob proposed to remove all existing spotted and speckled ones from the flock, and he would receive all such animals that might be born at the next lambing time. The proposal seemed so much in favor of Laban that he at once agreed to it, thinking he was getting the better end of the deal.
Regarding the use of rods that Jacob employed, the commentary states:
It was apparently thought by shepherds of the second millenium that if ewes saw before them a certain pattern during the mating season, their offspring would be born with such a pattern in their fleece. However, there is no biological evidence that such a practice in any way effects the coloration of offspring. The results were positive for Jacob, and despite his manipulation of the situation, he attributes his success to the Lord.
In Genesis 31:7-9 Jacob states to his wives, Yet your father has deceived me and changed my wages ten times, but God did not allow him to hurt me. If he said thus: The speckled shall be your wages, then all the flocks bore speckled. And if he said thus: The streaked shall be your wages, then all the flocks bore streaked. So God has taken away the livestock of your father and given them to me.
While using the rods represented Jacobs efforts to see that the flock bore the pattern he desired, Jacobs ultimate point of view is that ultimately it did not matter, God would have made the sheep the correct color or pattern to give them to Jacob. That God had restored to Jacob his wages that had been stolen over the many years by the deceitfulness of Laban.
Just like today, people may trust in God for an outcome in their lives, and we do all that we can do to produce this same outcome. For example you could trust God for a new job. Sending out resumes and going on job interviews would the be the physical efforts you go through in order to obtain the job. Jacob ultimately trusted God in the deal he made with Laban, and the rods (even though they dont have any power themselves) represent Jacobs own physical efforts toward what he was trusting in God for.