it means only write code that contributes something useful to what your application is trying to accomplish.
for connection errors and errors from query(), prepare(), and most execute() calls (except for duplicate or out of range errors when inserting/updating user submitted data), there's nothing the visitor to your site can do to recover from the error, they are due to programming mistakes or a database server that's not running, ... therefore, there's no point in writing any code for these cases. just let php catch the exceptions in these cases and display (when developing code/query(ies)) or log (when on a live/public server) the actual error information, so that you, the programmer/developer, will know when these type of errors are occurring, so that you can find and fix what's causing them.
the only types of database errors that the visitor to a site can do anything about are when inserting/updating duplicate or out of range visitor submitted data. this is the only case where having database error handling code in your application will do anything useful. you would catch the database exception, test the error number, setup a message telling the visitor exactly what was wrong with the data that they submitted, so that they can potentially submit a different value that will succeed.