Original: Born to a dog demon father and human mother, InuYasha is a half-dog demon who initially wants to use the power of the Sacred Shikon Jewel to become a full-fledged demon like his brother, Sesshomaru. Fifty years prior to the main era of the storyline though, Inuyasha fell in love with the priestess Kikyo, who guarded the jewel.
Simplified: Kagome learns that Inuyasha wants the jewel to become a full demon.