In a Taguchi design, the slope is the rate of change for the response relative to the signal factor. Usually your goal is to choose factor levels that meet a target slope. For each factor combination in a dynamic experiment, Minitab calculates the slope of the least squares fitted line for the signal-response data passing through the reference point (if specified).
For example, a group of scientists wants to know how five control factors affect a plant's rate of growth. They consider two noise factors, temperature and humidity. The slopes for this example provide estimates of the rate of change in plant growth because of temperature and humidity for each of the five control factors.