Pairwise testing aims to catch potential bugs that are present when specific pairs of items cause an issue. So for example a web form may work fine using Firefox. And the web form may work fine if the user selects England as the location. But it may have an error if both Firefox is used and England is selected. This pair causes an error where neither alone causes an error.
Orthogonal array testing (OATS) and combinatorial testing are enhanced versions of pairwise testing.