The block is a factor. The main aim of blocking is to reduce the unexplained variation (SSResidual)(SSResidual) of a design -compared to non-blocked design-. We are not interested in the block effect per se , rather we block when we suspect the the background "noise" would counfound the effect of the actual factor.
We group experimental units into "homogeneous" blocks where all levels of the main factor are equally represented. The analysis of variance of a Randomized Control Block design splits the residual term of an equivalent single factor Complete Randomized design in block and residual components. We should note, however, that the latter component has fewer degrees of freedom than in single factor CR designs, leading to higher estimates for MSResidual=SSResidual/d.f.MSResidual=SSResidual/d.f..