... 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? 你有興趣去那個國家工作嗎？
Italian food doesn't appeal to Jack; he only likes Chinese food. 杰克不喜歡意大利餐，他只喜歡中國餐。
This music is too old-fashioned to appeal to young people any longer. 這音樂太過時了，不能再吸引年輕人了。