Use it to emphasize you or someone else's lack of connection with a person or event. Despite the rumors, I have nothing to do with the company's decision.
Pro Tip 2/3
Disassociation
Expresses a strong desire to separate oneself from someone or something. She made it clear she wants nothing to do with the project anymore.
Pro Tip 3/3
Denial of Responsibility
Asserts that you are not responsible for an action or situation. I have nothing to do with the mistakes in the report.