Drupad was a prince. So after finishing his education he went back to his kingdom and later became the king. On the other side Drone was a Braahman. He was married to Kripee (sister of Kripaachaarya and daughter of Maharshi Shardwaan and Urvashee - an Apsaraa). He could not get anything to live up on for quite some time. 

They got a son also Ashwatthaamaa. When he was too young, he wanted to drink milk, but there was no milk in the house. So Kripee gave him flour mixed in water instead of milk. Drone saw it. He became extremely sad. He decided to go to his old time friend Drupad who said that "whatever is mine, half of it is yours". He went there and reminding him of his saying, asked only for one cow from him from his share of his belongings. But Drupad said "It was only child's talks said in a playful mood. How it could be possible that I could share my half wealth with you?"  and refused to give the cow to him. He was ready to give it as donation but not as Kripaa's share, while Kripaa didn't want donation, he wanted from his own share. Drone came back with an ill feeling in his heart, but this incident left the seed of enmity in Drupad's heart as well as in Drone's heart.

For the same reason Drupad did a Yagya to get a son who could kill Drone. When the Rishi wanted to offer Aahuti, he asked for his wife. Raajaa told that she was taking bath. It was getting late so the Rishi offered the Aahuti and incidentally that Aahuti was for a girl. So Agni Dev appeared from the Havan Kund carrying a beautiful girl. Though Raajaa was very happy to see that beautiful girl, but still since his aim was to get a son to kill Drone, so another Aahuti was offered. Another time Agni Dev appeared with a young man. He was named Dhrishtdyumn. The daughter was named Draupadee.