The popular "topic of your choice" option had been removed from the Common Application between 2013 and 2016, but it's now back again for the 2017-18 admissions cycle. Use this option if you have a story to share that doesn't quite fit into any of the options above. However, the first six topics are extremely broad with a lot of flexibility, so make sure your topic really can't be identified with one of them. Also, don't equate "topic of your choice" with a license to write a comedy routine or poem (you can submit such things via the "Additional Info" option). Essays written for this prompt still need to have substance and tell your reader something about you. Cleverness is fine, but don't be clever at the expense of meaningful content.
Write an essay in which you explain how [the author] builds an argument to persuade [his/her] audience that [author’s claim]. In your essay, analyze how [the author] uses one or more of the features listed above (or features of your own choice) to strengthen the logic and persuasiveness of [his/her] argument. Be sure that your analysis focuses on the most relevant features of the passage. Your essay should not explain whether you agree with [the author’s] claims, but rather explain how the author builds an argument to persuade [his/her] audience.