The Flanker Family Evolution: SU-27 to SU-33.
The SU-27 Flanker began its development as an answer to the F-15 Eagle, later to be one of the United States' most successful fighter aircraft. In line with Soviet technological limitations, the SU-27 was intended to counter the F-15's advanced radar and electronics suite with high maneuverability and close coordination with surface to air missiles and other aircraft like the Mig-29 Fulcrum. Exercises held between the US and India, which operates an upgraded Flanker variant known as the SU-30, indicate that the design is largely successful where it intended to be - the Flanker fighters are extremely acrobatic and nimble, and have been successfully used in several conflicts since the end of the Cold War.
The Flanker's success and general adaptability made its airframe an ideal choice for operating from then-building Soviet aircraft carriers. Even as the Soviet Union split apart, the SU33 continued development and entered service in the 1990's on Russia's sole carrier, the Admiral Kuznetsov.
China is rapidly building its military capabilities in order to be able to effectively defend its territory from modern militaries, and it is in effect rushing to deploy ships and aircraft that are of first-class quality. As such, in light of Chinese designers' inexperience with producing carrier based aircraft, it is not a surpise to find that they sought to buy the SU33 Flanker in the past, and when rebuffed, appear to have turned to reverse engineering the design based on a prototype purchased from the Ukraine.