Sesshoumaru is Inuyasha's older half-brother, though unlike him, he's a full-blooded dog demon. He looks down on Inuyasha for being half-demon and for hanging around humans, and he's arguably the strongest demon in the series—though even he couldn't beat Naraku when it came down to it. Fans call him the Lord of the Western Lands, though that title never actually shows up in the manga itself. He also has no real permanent home and, unusually for demons in this world, has zero interest in collecting Shikon Jewel shards.
Their father Inu-no-Taisho left Sesshoumaru the Tenseiga, a sword that can't hurt living things but can resurrect the dead. He got it instead of the Tessaiga—the one Inuyasha inherited, which can kill a hundred demons in a single swing. Their father apparently hoped this inheritance would teach Sesshoumaru some compassion. Naturally, Sesshoumaru thought Tenseiga was worthless and spent a lot of energy trying to take Tessaiga from his brother. When Naraku's incarnation Goshinki destroyed Tessaiga in battle, Sesshoumaru had Goshinki's fangs forged into Tokijin, an evil blade powerful enough for only him to wield.
Early on, Sesshoumaru is brutal and cruel, especially toward Inuyasha. But his character takes a turn when he meets Rin, a human orphan whose village was destroyed by demons. She found him injured in the woods and tried to help despite his rejection. Later, when she's nearly killed by Koga's wolves, Sesshoumaru uses Tenseiga to bring her back to life. After that, Rin becomes devoted to him, following him around and considering herself his servant—a strange dynamic given how much he claims to hate humans.
Content compiled by AnimeList.moe from publicly available sources.