Though not a federal standard, contiguity is the most common state-applied standard for district maps, and therefore is an important feature to be able to guarantee in any automated redistricting program. Put simply, one should be able to walk from any point in the district to any other point in the district without having to cross a district boundary.
Contiguity checks can be useful in other contexts, too. For example, when examining the changes made between a proposed district plan and its amended version in the redistricting process, it is relatively simple to generate statistics on, say, the people who were moved out of a particular district. But it’s possible that two different chunks of people were moved out, from opposite ends of the district and with different demographic profiles, or perhaps more than a dozen different chunks (see: changes to congressional district 5 in the Florida redistricting process). Sorting out the different groups can be done visually with a program like ArcGIS, but if you’re doing this process on a number of different districts in a number of different maps, it’d be nice to have an algorithm to separate out the pieces for you.