What is charge?

I did this static electricity experiment with my class. In the top picture, the two different materials attract. In the bottom picture, two identical materials repel when charged by friction. This is evidence that there are two types of static electricity which were named positive and negative charge. But what is charge? If mass is that thing which allows an object to feel a gravitational force, then charge is that thing which allows an object to experience an electromagnetic force, It is that hard to define! We can say what it does but not what it is. I like the treatment on this site http://amasci.com/elect/charge1.html