Stress is a physical quantity that averages over internal forces (e.g. van der Waals forces, Ionic bonding, collisions, ...) that neighbouring atoms/molecules of a material exert on each other.
If a force acts on an object, it causes stress inside the material. Stress behaves like a fluid in the sense that stress flows trough the material. Now, if there is a sharp corner, stress can't flow around it which causes a concentration of stress in that point.
If the stress in that region is to high, the material will fail. Therfore having round corners instead of sharp corners can make a structure stronger. The following picture from Wikipedia illustrates this quite well: