What goes wrong if I don't do that?

I believe if you don't use a slash at the end of the source directory, it will copy the _directory_, not just its contents.

    rsync code remote:/

I believe that results in remote:/code/app.js

    rsync code/ remote:/

I believe that results in remote:/app.js

Good explanation -- at the risk of mindlessly repeating you, my reason for the "always use trailing/ slashes/" suggestion is that the behaviour in that case has (for me at least) always been the scenario desired most often:

    rsync /some/where/local/ host:/another/place/remote/

The contents of local/ go into remote/

The trailing slash on the source expresses that you want to copy the contents of the source in the dest, otherwise you’ll copy the source itself (creating a subdirectory).