罢休 means 'to give up, to stop (a pursuit)' — it emphasizes ceasing an ongoing effort, often with the sense of 'letting the matter drop'. Compared to 放弃 (fàng qì), which is a neutral 'abandon/give up' for any goal or possession, 罢休 is more specific to stopping an action one has started and is often used in negative expressions like '不罢休' (refuse to give up). 死心 (sǐ xīn) is even more emotional, meaning to give up hope internally.