A resolution is another word for the topic of a debate round. It is most often used in American debate formats like Policy (Cross-Examination), Lincoln-Douglas, and Public Forum. Canadian and British formats usually call the same thing a motion. Functionally, there is no difference - a resolution is what the round is about.
How Resolutions Are Written
Resolutions in American formats often begin with 'Resolved:' followed by the topic statement. For example: 'Resolved: The United States federal government should substantially increase investment in renewable energy.' The affirmative team argues in favor of the resolution, and the negative team argues against it.
Season-Long Resolutions
Unlike parliamentary formats that use different motions each round, American formats often use the same resolution for an entire season or competitive period. That allows for deep research and evidence preparation, which is why Policy debate is so evidence-heavy and why cases are so long and detailed.