For a treatment term in an analysis of covariance, this represents the amount of information remaining on the term after adjusting for covariates. Usually the values will be around 0.8 to 0.9. A low value should be taken as a warning: either the measurements used as covariates have been affected by the treatments, which can occur when the measurements on covariates are taken after instead of before the experiment or the random allocation of treatments has been unfortunate in that some treatments are on units with generally low values of the covariates while others are on generally high ones.
For a residual term, the value indicates how much the covariates have improved the precision of the experiment. This is calculated by dividing the residual mean square into the value that would have been given if no covariates had been fitted. (See