Itsuki is Sensui's right hand man in carrying out Sensui's evil plan. Although he has strong psychic abilities, he needs another ability which can tear dimensions. That's where Kuwabara's part comes in. As he is the only one in Ningenki who can do something like that.
As for the way Sensui and Itsuki met, it was that as a youkai Itsuki tried to fight and beat Sensui. But he was unsuccessful, and was at Sensui's mercy because it so happened that he was a demon target of Sensui's. Before Sensui would kill him he was given one wish. And Itsuki wished to live one more day so he could watch the last episode of his favorite TV show... which just happened to be Sensui's too. After that, the two became close companions.
Throughout the series you can see how Itsuki is interested in Sensui by the way he watches his every move. Including emotions, weakness, fighting skills, etc.