Once your brand name or your brand logo is fully registered, you will receive your trademark certificate. It is an official document that proves your ownership of a given trademark. In most jurisdictions, you will receive an electronic certificate; however, it is possible to request a paper version as well.
After registration, you can start using the symbol ® to signal your brand's protection level.
Your trademark will protect you from any copycat attempts in those jurisdictions where you registered your mark. If you find there is a confusingly similar brand in the market, you will be able to approach them and ask them to adjust their branding, as they are infringing on your trademark. Sometimes, brands can do this unknowingly, so it's always a good idea to try resolving this issue amicably.
You can find more tips on the practical uses of your registered trademark in the category Using your trademark.