"The Lord said to her, 'Two nations are in your womb, and two peoples from within you will be separated; one people will be stronger than the other, and the older will serve the younger.'" NIV translation
God gave the answer to Rebekah's question and it would have been easy for her to understand except for the last part. When God told her that the older would serve the younger, that would have been hard for her to understand because that went against the normal order of things. She must have accepted it even though she did not understand and that is the very definition of trust (faith). We all have to ask ourselves if we are ready to trust God enough to accept things that we do not understand.
"When the time came for her to give birth, there were twin boys in her womb. The first to come out was red, and his whole body was like a hairy garment; so they named him Esau. After this, his brother came out, with his hand grasping Esau's heel; so he was named Jacob. Isaac was sixty years old when Rebekah gave birth to them." NIV translation
This was before the modern technology of ultrasounds and prenatal care. They would not have known that she was having twin boys until they were delivered. This would have served to build her up in her faith as she saw that what God had told her came to pass.
"The boys grew up, and Esau became a skillful hunter, a man of the open country, while Jacob was content to stay at home among the tents. Isaac, who had a taste for wild game, loved Esau, but Rebekah loved Jacob." NIV translation
As the boys grew up, Esau liked the outdoors like his father and so they grew closer. Meanwhile, Jacob liked to spend more time at home with mom so they grew closer. It is just a simple fact that we get closer to the people that we spend more time with. It should also be a reminder to us that, if we want to draw closer to God, we should spend more time with Him in prayer and study of His word.