The intercept in regression
The constant term in a regression ANOVA table tests whether the mean of the outcome measure is zero. It is usually not important if the significance test result in a positive outcome, but can be useful if the outcome is a difference.
For example suppose digit span forward and the GOAT tests are both measured at the same two times on the same person. We wish to see if the difference over time in digit span forward is explainable by the difference over time in the GOAT. This can be done by taking the difference between the two time points for each test score. Then we need to regress the GOAT difference on digit span forward difference.
In the output we now check the t-test for the constant (or intercept) term in the regression. Seeing if the constant term is zero tells us if there is a non-zero difference in digit span forward scores, averaged over individuals, even after accounting for their difference in GOAT scores.
See also: Everitt B, and Hay D. (1992) p.90-91 Talking About Statistics: A Psychologist’s Guide to Design and Analysis. Edward Arnold. This text looks at the intercept to see if the difference in dysphoria scores is the same across group (a group x dysphoria (covariate) interaction).