TL; DR What makes a chair a chair is its ability to sit. An object is only in its category of objects as long as it fulfills its defining use for people. A chair must be allowed to sit to be a chair, or it becomes nothing more than empty material. A chair is a chair because of its ability to provide seating.
A pouf can also be considered a chair, even though they don't share many qualities. If it is the essence of the “chair” that matters, then anything that fulfills the function you have designated for chairs can be considered a chair. A bucket can be used as a stool, a fish trap, a hat, etc., as long as it doesn't have the same use as a chair at the same time. When the chair is scratched, it ceases to be the same chair, as it loses some of its constituent particles.
All chairs in the everyday (sensitive) world are imperfect examples of the perfect form of a chair that exists in the (intelligible) world of forms. To understand what makes something a chair, one must consider what things are chairs. So, what makes a chair a chair is that it is an imperfect copy, or for example, of the shape of the chair, which participates in that way. It doesn't matter if chairs have their intrinsic shape or are copied from the perfect shape that exists in a heavenly kingdom; some modern philosophers declare that chairs don't exist at all and that there are only “particles” arranged in the form of chairs.
Notice that logically, the form predates the instances; if all the chairs in the world were destroyed, the chair form would continue to exist, only without instantiating. A chair is defined as a chair when used as such; otherwise, it is only based on someone's word. A chair is a chair because we have decided that a particular configuration of matter is used for that purpose.