Its function is to tell people that the graphic or text it marks is the trademark of this commodity or service, not the name or advertisement.
And "R" is the abbreviation of English "register", which means to "register" goods or services with this logo, that is, to tell people that the graphics or words marked by it are not only trademarks, but also registered trademarks, which are protected by national laws and may not be used by any other individual or organization without authorization.
The scope of legal protection of R is indeed stronger than that of TM.