Localised stress increase at a geometric discontinuity such as a hole, notch or shoulder.
The stress at a notch tip is higher than the nominal stress by a factor Kt, which depends on the geometry rather than on the material. A small hole in a plate under tension roughly triples the local stress.
For ductile materials under static load, local yielding redistributes the stress and the concentration is usually tolerable. For fatigue, and for any brittle material, it is not — the notch is where the crack starts.
Ignoring stress concentration in a fatigue calculation because the part passes a static check. Fatigue is driven by peak local stress.
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