What is AO222 based design in concept of design of CMOS cell library?
AO222 just means And-Or 2 2 2 which logically means: 3 2-input ands feeding into 1 3-input or.  

Most inverting complex gates are actually implemented in a single CMOS stage, but non-inverting gates, like the one you mention, need at least two stages.  AO222 is most likely made from a AOI222 and an inverter.

AOI222 = 3 2-input ands feeding into one 3-input or feeding into an inverter.  Implemented usually with a single stage complex CMOS gate.

Other examples are OAI32 (or and invert) or ao21 (the one just converts into skipping the first stage, so a single input goes to the or, the other two inputs go into an and gate, then the or).

Below is a picture with a few logic diagrams to help explain: