The total stress experienced locally in a part is a summation of the residual stress and the externally applied stress. The residual stress could be of a similar magnitude to the applied stress, making a significant impact on the part during service.
Pushes the material together
Generally favorable
Can slow crack propagation, thus extending the life of the part
Can counteract applied tensile loads keeping a crack closed
Pulls the material apart
Generally not favorable
Can increase cracking