Who is sephiroth
Sephiroth is the Son of Lucrecia and Hojo. He was known to be born from JENOVA, a life form that tried to destroy the planet, but that was only a theory by Professor Gast.
And that's why you should never eat cookies without milk...
Anyway on with Kadaj
When Sephiroth was defeated by Cloud at the end of FF7 he entered the life stream. But Sephiroth (being Sephiroth) refused to go into the life stream and he broke up into three remnants of himself.
There is Yazoo, Loz and Kadaj...There not completely Sephy They have a 50% mind of there own...When the film (advent Children) starts they are 2 years of age even though they look much older than 2.
Kadaj is the leader of the SHM ( the silvered-haired men), Although he is youngest (16) and Yazoo and Loz are much older ( 20-22) he is the most charismatic so his brothers mostly rely on him for things...
Kadaj is constantly on a search for his "mother" This is because he is infact 2 years of age and he wants a mother to love for him like all kids need...But alas, Sephiroth kicks in his part and "Jenova" is what Sephiroth needs to come back so that's why Kadaj thinks that "mother" is Jenova (which it isn't he doesnt have a mother :S).
Infact Kadaj hates Sephiroth due to Jelousy he knows his "mother/Jenova" wants Sephiroth back and he thinks that "jenova" wants Sephiroth more than him ( aww :( I would Choose Kadaj over Sephiroth anyday ;)..)
Sephiroth is the last boss in Final Fantasy VII and is a really strong guy made from Jenova. He was really helpful to the Shinra Company, but as he found out he was made from Jenova, he got angry and hated everything except his mother, Jenova. He comes back in the movie Advent Children with Kadaj receiving blood from the head of Jenova. (You should really see the move, it's MEAN!)