This clause means that if your use of Dropbox causes legal problems for the company, you are financially responsible for defending them and paying any costs or damages they incur.
Dropbox's terms grant the company a broad license to your uploaded content to operate the service, and limit the company's liability for data loss or service interruptions. US users are required to resolve disputes through binding arbitration and waive the right to participate in class action lawsuits, significantly limiting legal recourse. You can opt out of arbitration by sending written notice to Dropbox within 30 days of first agreeing to these terms.