Most law schools give applicants the opportunity to write supplemental essays. While they're listed as optional, it's best to submit an essay, rather than leaving the school wondering why you didn't take the time to do so.
Optional essay topics should never duplicate your personal statement or addenda.
While some schools allow for creativity (Georgetown's "Top 10 List" and the University of Michigan's list of nine prompts to choose from for example), many fall into the following categories:
Why this law school?
Take time to research and write about what connects you to this particular law school. What are specifics about the program that you feel offer you the best opportunity to pursue the legal education of interest to you. Are there particular faculty with whom you'd like to work? Do they offer clinical experiences or other programs of interest? This space is not for general flattery ("Your law school offers the best clinical programs in the geographic region."), but rather a chance to connect yourself to the school.
Diversity Statement:
Law schools will often give applicants the opportunity to talk about an aspect of their background that is diverse, and which will help them contribute to the class the law school is building. Some tips for approaching the diversity statement:
The statement should not repeat the personal statement. If your personal statement relates to aspects of your diversity or identity, you'll need to write a different personal statement or explore another diversity theme for the optional essay.
Diversity has many different meanings, in addition to common identity-based aspects.
Talk about how diversity has played a part in your decision to go to law school, or how your diverse self can have an impact on your attendance in law school and the law profession.
Don't force the diversity statement just to write another essay or writing sample.
If you have questions, talk to a professor or the prelaw advisor to talk through ideas.