Irulan is the Emperor's eldest daughter and guess what? She's quite the looker. Didn't see that coming now, did you?
Paul marries Irulan to secure his position as ruler of the universe (more or less), though he saves his love for Chani. Irulan will go on to write many history books about the life of Muad'Dib and the people surrounding him. Excerpts from these histories provide the introductions to most of the chapters in Dune.