The point through which a transverse load must pass to produce bending without twisting.
For a symmetric section the shear center is the centroid, so this never comes up. For channels and angles — which are not symmetric — the shear center lies outside the section, and a load applied through the centroid twists the member as well as bending it.
The practical consequence is that a channel loaded through its centroid will twist, so channels used as beams are usually braced or loaded through the shear center.
Loading a channel beam through its centroid and being surprised by the twist. The load must pass through the shear center instead.
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