A personal story is a story from someone's life. It could be how they overcame difficulties or how they reached the place where they are today. It could be something as simple as a scene the writer observed a few days ago that has relevance to their topic and their audience.
Many personal stories involve overcoming difficulties. For example, you might write a story about a time when you couldn't manage your time well. You were always busy and had many things to do, but no free time to do what you enjoyed. This is the setting of the story. You then discovered a very simple and handy technique for managing time better, which helped you get more done and have more time to yourself.
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