The key achievement is that entropy defined by Clausius dS=dQrev
/T is a state property.
In general, you can imagine that to predict what is going to happen next, you need to know everything that happened before. However, the special property of a state variable is that to make a prediction, you just need to know it at one moment in time. (That's the rough idea.)
An example of something that isn't a state property is the work done on an object - that depends on the path through which you moved an object.
Mathematically, he discovered what is called an "integrating factor". http://en.wikipedia.org/wiki/Integrating_factor