“Jìxù” is a high-frequency word used in virtually all aspects of modern life. It's neutral in tone and can be used in both formal and informal situations.
In Conversation: Used to prompt someone to continue speaking after an interruption. For example, if your phone rings while a friend is telling a story, you might say, “你继续说 (Nǐ jìxù shuō)” - “Please, go on.”
At Work or School: It's used to indicate the resumption of an activity. A manager might say, “我们休息十分钟,然后继续开会 (Wǒmen xiūxi shí fēnzhōng, ránhòu jìxù kāihuì)” - “We'll take a ten-minute break, then continue the meeting.”
As Encouragement: As mentioned above, “继续加油! (Jìxù jiāyóu!)” is a staple phrase used to cheer on friends, colleagues, or athletes.
Describing an Ongoing State: It can describe a continuous, uninterrupted state, especially in narrative. For example, “雨继续下了一整夜 (Yǔ jìxù xiàle yī zhěng yè)” - “The rain continued to fall for the whole night.”