Despite a lot of intensive research in the field of polymer nanofibers as wound-healing and tissue-regeneration materials, the behavior of cells in contact with nanofibers in vitro as well as in vivo is still not well understood. However, this knowledge is crucial for the design of nanofibrillar materials that are suitable for biomedical applications. Therefore, in this study, we present the preparation of poly(vinyl alcohol) (PVA) nanofibers from a physico-chemically characterized polymer solution by electrospinning together with a stabilization method to preserve the morphology of the nanofibers in aqueous conditions. An investigation of the effects of a nanofibrillar scaffold on the growth of human keratinocytes showed that randomly oriented PVA nanofibers delay the keratinocytes' adhesion but improve their strength, greatly alter their morphology, increase their metabolic activity, and limit their mobility. We have shown that due to the small interfiber pores, the whole cells are unable to penetrate into nanofibrillar network efficiently. However, flexible cell parts can penetrate into the nanofibrillar network, whereas the cell nuclei stay on the surface of electrospun scaffold. Additional reason for poor cell mobility is random orientation of nanofibers, which does not provide continuous routes for successful cell infiltration. Therefore, nanofibrillar support with nanosized interfiber pores could potentially be used to enable an efficient cell proliferation and accelerate surface-wound healing, but not for three-dimensional tissue regeneration. Finally, we showed that aligned nanofibers can successfully direct the migration and proliferation of cells, which is a crucial property of nanomaterials for the successful regeneration of tissues with a highly organized structure.