Select Fit intercept to include the intercept (also called the constant) in the regression model. In most cases, you should include the constant in the model.
A possible reason to remove the constant is when you can assume that the response is 0 when the predictor values equal 0. For example, consider a model that predicts calories based on the fat, protein, and carbohydrate contents of a food. When the fat, protein, and carbohydrates are 0, the number of calories will also be 0 (or very close to 0).
When you choose not include the constant, Minitab does not display the R^{2} statistics. Use S instead of the R^{2} statistics to evaluate the fit of models.