This is an old English name for the city we now call Beijing, the capital of China. English used Peking for hundreds of years, so you still meet it on old maps, in older books, and in a few names that never fully changed: Peking duck, Peking opera, and Peking University, which kept the old spelling in English. The city did not move and the Chinese name 北京 did not change; English only changed the way it wrote the sounds. The older spelling kept a k from an older Mandarin pronunciation; modern Beijing writes that part more like an English j. Though actually, students sometimes mix this up with Beiping (北平), a different Chinese name the city used in the early twentieth century. That is a Chinese renaming story, not this English spelling. In new English, say Beijing unless you are using one of those frozen old names.