Show your understanding
When you are asked to write in your own words, your instructor wants you to demonstrate your comprehension of the material that you have listened to or read. This means that not only can you not just repeat the information word for word, you also have to do more than simply change the word order and order in which you present the information.
In addition to playing around with your choice of the vocabulary and sentence structure when writing, you will also have to include your personal interpretation of the information. This is writing in your own words.
When you write in your own words, you show that you have understood the material and demonstrate the skills you have gained. Moreover, putting information in your own words will also help you make better sense of what you have read.