G'MIC Reference documentation assumes knowledge as it was written by scientists for scientists.
This page is intended to make it more user friendly.
Many effects require finding the "best" result for small patches all at the same time, technically that is a Partial Differential Equation (PDE), an equation about how each pixel should look relative to its neighbours. This equation is the same everywhere so looks nice and simple mathematically but to solve all of those small patch equations at the same time you need to start at the edges and work inwards. Boundary conditions are the bits at the edge which do not change. Often in GMIC that means around the frame of the image.
What do the options actually do:
The GIMP plug-in has a filter Various / Custom Code. You can find a function then experiment with the different settings and see them in action.