The phrase "to burn the chocolate" means that you have cooked or heated the chocolate for too long, causing it to become dark and bitter. Full definition
Ideally do this with a glass bowl over a pot of boiling water so you do it gently and don't burn the chocolate. (happysugarhabits.com)
Carefully melt the mixture over low heat, stirring constantly to avoid burning the chocolate. (seitanismymotor.com)
Whenever I bake cupcakes or a cake with chocolate chips I definitely fear that sticky burnt chocolate mess at the bottom. (cinnamonspiceandeverythingnice.com)