天主教 is Catholicism; adding 徒 makes it 'Catholic person.' Similarly: 基督教徒 (Protestant), 佛教徒 (Buddhist), 伊斯兰教徒 (Muslim). The suffix 徒 means follower/disciple.
history
天主 (Lord of Heaven) was the Chinese translation chosen by Jesuit missionaries like Matteo Ricci in the 16th century, connecting Catholic theology with the Chinese concept of 天 (heaven).
