Original sentence: Here the summation is over the possible states i the system can be in given its description and the Pi is the proability for the system to be in state i.When given some incompletely specified system, the entropy is defined as the amount of information needed to  to completely specify the state of the system, given its incomplete description
Edited sentence: Here the summation is over the possible exact states i the system can be in given its incomplete description and the Pi is the probability for the system to be in state i.In case of thermodynamics, the incomplete description is called a macrostate, which can consist of a specification of the volume, internal energy and number of molecules in the system.The exact states the system can be in are the many particle quantum states the molecules can be in.When given some incompletely specified system, the entropy is defined as the amount of information needed to  exactly specify the state of the system, given some incomplete description