... different music appeals to different generations... (Para. 4)
Meaning: ... different generations are interested in different kinds of music.
appeal: vi. please, attract, interest
Please notice that "appeal" in this sense is usually following by the preposition "to".
Does the idea of working in that country appeal to you? 你有兴趣去那个国家工作吗？
Italian food doesn't appeal to Jack; he only likes Chinese food. 杰克不喜欢意大利餐，他只喜欢中国餐。
This music is too old-fashioned to appeal to young people any longer. 这音乐太过时了，不能再吸引年轻人了。