"Armaan" as the title signifies is the film about one's desire and hopes and how a son goes to fulfill his father´s dream. Dr. Siddharth Sinha (Amitabh Bachchan), a philanthropist, who owns a hospital and has a dream to expand it into a state of the art hospital and is on a lookout for some funds to achieve the cause. Dr. Akash Sinha (Anil Kapoor), a respected neurosurgeon, is equally devoted to help realize his father´s dream. Enter Neha Mathur (Gracy Singh), an anesthetist, who joins the hospital as an assistant to Akash Sinha. Their cordial relation starts blossoming into love with every surgery they perform together and how they realize they have so many things in common. Enter Soniya Kapoor (Preity Zinta), a spoilt daughter of a business tycoon Gulshan Kapoor (Randhir Kapoor), a girl raised in richness but with absence of love.
Soniya falls for Akash and wants to marry him. To fulfill his daughter´s wish, Gulshan Kapoor strikes a deal with Dr. Siddharth Sinha. He is ready to finance the hospital project on the condition that Akash marries her daughter. Siddharth Sinha rejects the deal. Already suffering from high stress, an unfortunate incident leads to the death of Siddharth Sinha and that leaves Akash helpless. Now, Akash has only one goal and that is to fulfill his father's dream and for this cause, he has to sacrifice the bond of love he shares with Neha. He enters into an agreement with Gulshan Kapoor and gets married to Soniya. From here on it is about the relationship between the three characters and how Akash sacrifices everything towards fulfilling his father´s dream. Through the course of the movie leading to the climax, Akash performs various surgeries and the director shows how each surgery relates to a medical victory for Akash, both as a neurosurgeon and as a human being.