In rules parlance, a region is a set of rook-wise connected intersections. Note that whether these intersections are black, white, or empty do not factor in the definition of region.
More formally, a go board of n lines by n lines can be seen as a two-dimensional n x n grid graph. Then a region is a connected subgraph of this grid graph.
Note that a chain is a kind of region.
Region also has a related usage as locale.