After he lost a battle to InuYasha, Sesshoumaru was severly wounded and ended up alone in the forest. Rin (a little girl who hadn't spoken since her parents had been killed by wolves) found him there, and tried to help by bringing him some food.
A bit later, Rin's village was attacked by wolves, and they (the wolves) killed her. Sesshoumaru (after recovering) found her, dead, and used Tenseiga to bring her back to life.
Since then, Rin has followed Sesshoumaru everywhere, and she even started speaking again. In a later episode Rin is kidnapped, and Sesshoumaru rescues her.
No one knows for sure why Sesshoumaru helped Rin (maybe he felt he owed her something for her earlier help, or maybe he was just in a good mood), but whatever the case, Rin has brought out a new side to our beloved Sesshy.