When he was little he hated Kenshin for taking away his siter's happiness. Then after witnessing his sister's death ( he was 10 ), he vowed revenge.
Little Enishi grows up and begins his plans for revenge after Kyoto Arc. In the manga it occurs right after Kenshin and everyone returns from Kyoto. In the Anime it takes quite a bit longer.

Enishi is basically insane. He has the ability to see and hear his sister. He also has some form of morals and honor.

Enishi first met Kenshin shortly after Kenshin's marriage to Tomoe; Enishi's elder sister. Enishi had protested Tomoe's previous engagement (to the man killed at the end of manga 19), and outright hated her involvement with Battousai. Judging from his birthdate, he was about 10 at the time. He was working as a contact in Edo when he went to pay a visit to his sister. It was not entirely to see Tomoe, however, because his employers had sent him to spy on the Battousai. He hated Kenshin , and ran out on his sister.

His return was rather ill-timed. He came back just in time to see Hitokiri Battousai, in a fight with Tomoe's kidnappers, accidentally slash Tomoe in the back with his katana. Tomoe died, and Enishi was led to believe that Kenshin had murdered her. He returned as an adult to avenge his sister's death and murder someone close to Kenshin.
After Tomoe died, Enishi was adopted by a well-meaning, well-off family. Jealous of their happiness, he killed them. He then used this money to get his start in the crime ring. He's actually the one who sold that big boat to Shishio.

Being a mafia boss isn't important to Enishi, however. He states in the manga that as soon as his Jinchuu (revenge) is carried out, he will turn over his organization to his second-in-command. He explains that he simply needed the funds for his revenge, and arms-dealing was convenient.

After his confrontation with Kenshin on the island, Enishi collapsed. He was arrested for numerous crimes, but shortly after receiving his sister's diary, disappeared from the ship that carried him to jail. He met up with his father (although he did not apparently recognize him), and was never heard from again.