The registered symbol is used to give notice for people that a specific product has been registered with a national trademark office. In some countries, if the product is not a registered trademark, then it is prohibited by the law to use this symbol. If the product is not officially registered, then you can use other symbols like ™ or SM.
The proper way to display the registered trademark symbol is to place it directly after the mark in superscript style, but it's not usually legally required. This symbol was introduced in the United States of America in the Trademark Act in 1946.