I googled "gauge theory for dummies", but got nothing. Understanding the "Gauge theory" is not that easy. But the two key words might be invarianc and measurement. When we measure any variable in a field which varies depending on space-time, we may want to assure any transformation does not affect the measurements. identical observable quantities. We call the transformation as Gauge transformation
Here is a couple of key sentences from wiki.
In field theories, different configurations of the unobservable fields can result in identical observable quantities. A transformation from one such field configuration to another is called a gauge transformation; the lack of change in the measurable quantities, despite the field being transformed, is a property called gauge invariance. Since any kind of invariance under a field transformation is considered a symmetry, gauge invariance is sometimes called gauge symmetry. Generally, any theory that has the property of gauge invariance is considered a gauge theory.
The Cartesian coordinate grid on this square has been distorted by a coordinate transformation, so that there is a nonlinear relationship between the old (x,y) coordinates and the new ones. Einstein's equations of general relativity are still valid in the new coordinate system. Such changes of coordinate system are the gauge transformations of general relativity.
NOTE: Above information has been taken from wikipedia and/or official websites of topics.