This is a great question. These words take place in chapter 12 of the book. A little context will be important to understand what is going on. By this time of the book, Amir is in love with Soraya. However, he is afraid of general Taheri, her father. Moreover, Amir is a shy person. While the general is away, he talks with Soraya and they fall in love. Meanwhile, Baba is diagnosed with cancer and it spreads to his brain. All know that there is little time. Amir ask Baba to go to the general to ask for Soraya's hand in marriage. He does and all is set.
In this context, these words appear. Amir, on the one hand, is thankful to Baba for his support. Moreover, he is deeply in love with Soraya as he thinks of their future together. On the other hand, the future is painful to look at, because Baba will not be there.
In light of this point, Amir is coming to terms that the future will look different. Baba, who has played a huge role, will no longer be present. Moreover, by this time of the book Amir and Baba have gotten to an understanding where there is mutual love and respect.