Stress in thin films are forces being induced by the substrate the film is deposited on, particularly when the crystal structure of the materials differs a lot. The lattice of a thin film will be distorted by the influence of the substrate, which means in fact "stress" for the film. This stress may have significant influence on the substrate/film interface and lead to delamination in the worst case.
Extrinsic stresses arise due to substate-thin film mismatch in (crystallographic structure, thermal expansion chemical reactivity), and their dependence on temperture and many factors relating to the differences in the physical properties of the substrate and thin film.
Intrinsic stresses are due to the deposition conditions, and build up in the thin film while they are growing.
You can have compressive or tensile stresses in the film. These can be estimated, and also measured, and seen through other methods X-ray diffraction studies.
As suggest the worst case with stresses in the films, they will buckle, peel away, having very poor adhesion, and also delaminate from the substrate.
There are many books on Thin film Technology, and also review papers written on different thin film materials deposited by different techniques under different conditons, and deal with the topic. It is always useful to consult them.