In life Kikyo was a powerful priestess, entrusted with guarding and purifying the Shikon no Tama. Eventually she fell in love with Inu-Yasha, the hanyou who constantly tried to steal the jewel in order to become a full youkai. Offering to give Inu-Yasha the Shikon no Tama to become human, she was tricked on the day she was to give him the jewel and attacked by Naraku in Inu-Yasha's form. In turn, she sealed him to the Goshinboku Tree before dying herself. As her final wish, her remains were burned along with the Shikon no Tama.
Fifty years passed before Kagome ended up in Sengoku Jidai and revived Inu-Yasha. An ogress named Urasue stole Kikyo's remains and used them to recreate her body. Since her soul had already been reborn in Kagome, Urasue kidnapped Kagome and used a spell to transfer her soul back to Kikyo. Sparing details--I don't want to give anything away, Kikyo winds up surviving with only her hatred of Inu-Yasha to keep her going. She continues to be a thorn in his side; loving him, yet determined to kill him at the same time.