The business registration (Gewerbeanmeldung) is when you register your business at the Gewerbeamt. This is how you get a trade licence (Gewerbeschein) and register for the trade tax (Gewerbesteuer).
Freelancers (Freiberufler) do not need to do the Gewerbeanmeldung.
How to do the Gewerbeanmeldung
If you close your business or leave Germany, you must deregister your business. This is called the Gewerbeabmeldung.