to 'understand' mean you have perceived an idea mentally while to "know" may mean that you have experienced something or you are aware of the fact/idea of the information. here, if you heard someone speaking english and you can interpret or translate what he's saying, you would normally say: "I understand what he's saying." but if you are able to determine or define what he's saying all about, you would say: "I know what he's saying." "realize" would mean: to make real or give reality to something. it is like getting the meaning of something or getting the whole picture (in your mind). ex: "I realized that if I invest something for my kids, they would have a happy life in the future." here, you're imagining or assuming the possible things that might take place for the good action your planning now. :)

如果别人对你讲一件事，例如：“从前有个山，山里有个庙……”。然后你就可以说：“我知道这个故事”，那么这时候你就可以用“I know". 如果有人对你阐述一个观点或者给你讲一道题，例如：“3的平方是9，你知道吗？”这时你可以说：“我知道”。那么你可以用“I understand". 如果有人问你："你有没有察觉到我变得漂亮了"?那么这时你就可以回答“Yes,I do realized that you became very beautiful." 这三个词的区别就在于：知道、懂、察觉。 希望我的回答可以帮助你。

I think it is difficult to explain. It is best - for speaking - to just use the word "know" - it will usually be correct if you speak this word. There is little difference in meaning. The difference is emphasis. "Realize" = this is usually not about academic knowledge but about other people's feelings or situations or if there is a problem. It is often used to make a contrast..... "I realize English is difficult, but you can do it!" "understand" = this word emphasizes that you have learned this information My opinion, as a native speaker - but not as a language expert, is that there is little difference in meaning - but there is a difference in emphasis. My adivice - is that when speaking - the "safest" word for you to use is "know" because it will cover the most area. "I know that" "I don't know this" ..... You can use "understand" with situations when you need an explanation..... for example...... "I don't understand the difference between know, realize, and undersand. can you explain teh difference." oh, I hope that helps. my notes are a litte messy. good luck.