Capsaicin is a natural extract from chilli peppers. It is the part of the chili that gives the burning feeling in your mouth. So why would you put it on such a sensitive area as your vulva?
We all know how hot a curry can be. But we also know that people who eat curry every day get used to eating hot food and can eat chillis easily without discomfort. Their mouth becomes desensitized to the burning feeling.
Something similar happens when capsaicin (chilli) is put on painful vulval skin. The first time it is used, there is a sudden release of pain chemicals from nerves, and a strong burning feeling. However, over time, when used regularly, the nerves release less and less of the pain chemicals and the vulval skin becomes less sensitive.