Zhuyin (or Bopomofo, named after the first four letters in its alphabet, ㄅ, ㄆ, ㄇ, and ㄈ) is a modern script invented to transcribe the sounds of Chinese characters. It is used mainly in Taiwan, as the PRC uses Pinyin, a Latin script. It most often used as a ruby gloss above Chinese words to indicate their pronunciation. There are also several tone markers which are placed after the character, rather than above like Pinyin tone markers.
The pronunciations of some Bopomofo characters vary depending upon their position within the syllable, but for the purposes of the quiz above, they are as follows, transcribed into Pinyin:
See Wikipedia for a more detailed list.