RIAA stands for Recording Industry Association of America. The RIAA is the trade association representing the American recorded music industry. Its members include record labels and distributors.
The RIAA lists the following as its goals as: to protect intellectual property rights and the First Amendment rights of artists, to perform research about the music industry, and to monitor and review relevant laws, regulations and policies.
When a song is given a certification status such as "platinum", this is issued by the RIAA.
For more information, visit the RIAA's website here.