What is the 'install' directory in my catkin workspace?

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It's not an issue to have this directory in your catkin workspace. Its name is really self-explanatory : it's the folder where you install your targets once they've been built. You can find this in the catkin wiki.

Now why do you have this folder and if you don't want it anymore is related to your CMakeLists.txt. If you use the catkin command catkin_create_pkg you would get this template of CMakeLists.txt (only the relevant part) :

## Mark libraries for installation
## See http://docs.ros.org/melodic/api/catkin/html/howto/format1/building_libraries.html
# install(TARGETS ${PROJECT_NAME}
#   ARCHIVE DESTINATION ${CATKIN_PACKAGE_LIB_DESTINATION}
#   LIBRARY DESTINATION ${CATKIN_PACKAGE_LIB_DESTINATION}
#   RUNTIME DESTINATION ${CATKIN_GLOBAL_BIN_DESTINATION}
# )

It's all commented by default but if you uncomment it then the install folder is created after running make install. So just check your CMakeLists.txt to find all the instructions install().

See #q253363 for a similar question.