i know that the base station controls the power output of the mobile, keeping the GSM power level sufficient to maintain a good signal to noise ratio, while not too high to reduce interference, overloading, and also to preserve the battery life. now i want to know what is a power class number? For example GSM power class?
Based on the wording of the question, it appears OP was reading this article.
My interpretation of "Power Class" from this article is that it is a phone specification. Phone manufacturers will design their phones to meet a certain power class level. The phone will then tell the station what power class it belongs to. With that information, the base station can then decide how to handle the phone.
Power class would also be a useful metric for phone designers. Instead of picking parts that will produce a specific maximum dB power, they would look to meet a certain power class. It's simply a way of bucketing a range of powers for standardization.