Think of the word on as indicating continuation or endurance, live on to continue to exist or be remembered, go on to proceed or continue, move on to progress or advance, pass on to transmit or convey play on to continue playing, especially in sports.
把 "繼續"(on)這個詞想象成表示延續或耐力,"繼續"(live on)表示繼續存在或被記住,"繼續"(go on)表示繼續進行或繼續,"繼續"(move on)表示進步或前進,"繼續"(pass on)表示傳遞或傳達。