Definitions
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 n. Given a smooth closed curve C on a surface M, and picking any point P on that curve, the holonomy of C in M is the angle by which some vector turns as it is parallel transported along the curve C from point P all the way around and back to point P.
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Examples

Tracy Houston: Recently I came across the term ‘holonomy.’
Gaining a Competitive Edge Through Systems Thinking  Impact Lab

This can be seen as an instance of the more general notion of the holonomy of a closed curve, a notion that has come to the fore in contemporary formulations of gauge theories including electromagnetism in terms of fiber bundles (Healey (2007)).

It is possible to stabilize the moduli without fluxes in Mtheory compactified on singular manifolds with G_2 holonomy.
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