What is the applypatch tool and how does one use it?
diff and patch are Unix/Linux commands used to easily check for differences, send updates to huge files by shipping only the differences, etc. (see Wikipedia). They are mostly used in development (to update source code), but can also serve practical purposes in non-development environments.

applypatch is one of those patch-tools on Android, and used e.g. for minor updates (OTA and the like). So it is most likely not intended for the "normal end user" to deal with it directly.