Rashi says that after G-d told Noach to be fruitful and multiply (in the previous aliyah), Noach feared that his descendants might be destroyed in a subsequent mabul. Therefore, this aliyah begins with G-d promising not to destroy the world with another mabul.

G-d signifies His covenant by creating the rainbow. In the book "Hayom-Yom", in the entry of the day that this aliyah corresponds to (Thursday), it says that we should make the appropriate brocho (on page 87 of the siddur Tehillat Hashem), upon seeing a rainbow.